Resourcesdown chevron
Testimonials
Plans
Sign in
Sign up
Resourcesright arrow
Testimonials
Plans
Bytelearn - cat image with glassesAI tutor

Welcome to Bytelearn!

Let’s check out your problem:

Solve the exponential equation for x. {:[27^(5x-4)=81^(7x-2)],[x=◻]:}

Solve the exponential equation for x x .\newline275x−4=817x−2x=□ \begin{array}{l} 27^{5 x-4}=81^{7 x-2} \\ x=\square \end{array}

View step-by-step helpView step-by-step help
Homeright chevron icon
Math Problemsright chevron icon
Algebra 1right chevron icon
Compare linear, exponential, and quadratic growthright chevron icon

Full solution

Q. Solve the exponential equation for x x .\newline275x−4=817x−2x=□ \begin{array}{l} 27^{5 x-4}=81^{7 x-2} \\ x=\square \end{array}
  1. Recognize powers of 33: Recognize that both 2727 and 8181 are powers of 33. 2727 is 333^3 and 8181 is 343^4.\newlineRewrite the equation using the base of 33.\newline275x−4=817x−227^{5x-4} = 81^{7x-2}\newline⇒(33)5x−4=(34)7x−2\Rightarrow (3^3)^{5x-4} = (3^4)^{7x-2}
  2. Rewrite equation using base of 33: Apply the power of a power rule, which states that (ab)c=a(b∗c)(a^b)^c = a^{(b*c)}.$33\$3^3^{(55x−4-4)} = 343^4^{(77x−2-2)}\)⇒3(3∗(5x−4))=3(4∗(7x−2))\Rightarrow 3^{(3*(5x-4))} = 3^{(4*(7x-2))}
  3. Apply power of a power rule: Simplify the exponents on both sides.\newline33(5x−4)=34(7x−2)3^{3(5x-4)} = 3^{4(7x-2)}\newline⇒315x−12=328x−8\Rightarrow 3^{15x-12} = 3^{28x-8}
  4. Simplify exponents: Since the bases are the same, set the exponents equal to each other. 15x−12=28x−815x - 12 = 28x - 8
  5. Set exponents equal: Solve for xx by first moving the xx terms to one side and the constants to the other side.\newlineSubtract 15x15x from both sides:\newline15x−12−15x=28x−8−15x15x - 12 - 15x = 28x - 8 - 15x\newline⇒−12=13x−8\Rightarrow -12 = 13x - 8\newlineAdd 88 to both sides:\newline−12+8=13x−8+8-12 + 8 = 13x - 8 + 8\newline⇒−4=13x\Rightarrow -4 = 13x
  6. Solve for x: Divide both sides by 1313 to solve for x.\newline−413=13x13-\frac{4}{13} = \frac{13x}{13}\newline⇒x=−413\Rightarrow x = -\frac{4}{13}

More problems from Compare linear, exponential, and quadratic growth

Question
Jill bought a used motorcycle from a seller online for $1,200. The seller will charge her $5 a day to store the motorcycle at his house until she is able to pick it up. You can use a function to describe the total amount of money Jill will owe the seller if she waits xx days to pick up the motorcycle.\newlineWrite an equation for the function. If it is linear, write it in the form g(x)=mx+bg(x) = mx + b. If it is exponential, write it in the form g(x)=a(b)xg(x) = a(b)^x.\newlineg(x)=‾g(x) = \underline{\hspace{3em}}
Get tutor helpright-arrow

Posted 8 months ago

Question
How does f(t)=−2t−7f(t)=-2t-7 change over the interval from t=−7t=-7 to t=−6t=-6?\newlineChoices:\newline[f(t) decreases by 2]\left[\text{f(t) decreases by } 2\right]\newline[f(t) increases by 2]\left[\text{f(t) increases by } 2\right]\newline[f(t) increases by 200%]\left[\text{f(t) increases by } 200\%\right]\newline[f(t) decreases by a factor of 2]\left[\text{f(t) decreases by a factor of } 2\right]
Get tutor helpright-arrow

Posted 8 months ago

Question
How does g(t)=9tg(t)=9^t change over the interval from t=1t=1 to t=3t=3?\newlineChoices: \newline[g(t) decreases by a factor of 81]\left[\text{g(t) decreases by a factor of } 81\right]\newline[g(t) increases by a factor of 81]\left[\text{g(t) increases by a factor of } 81\right]\newline[g(t) increases by 18%]\left[\text{g(t) increases by } 18\%\right]\newline[g(t) decreases by 9%]\left[\text{g(t) decreases by } 9\%\right]
Get tutor helpright-arrow

Posted 8 months ago

Question
Both of these functions grow as xx gets larger and larger. Which function eventually exceeds the other?\newline Choices:\newline(A)f(x)=8x+3.3(A)f(x) = 8x + 3.3\newline(B)g(x)=3.3x−5(B)g(x) = 3.3^x - 5
Get tutor helpright-arrow

Posted 9 months ago

Question
Both of these functions grow as x x gets larger and larger. Which function eventually exceeds the other?\newlineChoices:\newline(A) f(x)=2x+9(A) \ f(x) = 2x + 9 \newline(B) g(x)=2x(B)\ g(x) = 2^x
Get tutor helpright-arrow

Posted 9 months ago

Question
The functions f(x) f(x) and g(x) g(x) are differentiable. \newlineThe function h(x) h(x) is defined as: h(x)=g(x)f(x) h(x)=\frac{g(x)}{f(x)} \newlineIf f(8)=1 f(8)=1 , f′(8)=−6 f'(8)=-6 , g(8)=8 g(8)=8 , and g′(8)=−10 g'(8)=-10 , what is h′(8) h'(8) ? \newlineSimplify any fractions. \newlineh′(8)= h'(8)= ______
Get tutor helpright-arrow

Posted 8 months ago

Question
The functions p(x) p(x) and q(x) q(x) are differentiable. \newlineThe function r(x) r(x) is defined as: r(x)=p(x)q(x) r(x)= \frac{p(x)}{q(x)} \newlineIf p(3)=2 p(3)= 2 , p′(3)=4 p'(3)= 4 , q(3)=6 q(3)= 6 , and q′(3)=9 q'(3)= 9 , what is r′(3) r'(3) ? \newlineSimplify any fractions. \newliner′(3)= r'(3)= _____
Get tutor helpright-arrow

Posted 9 months ago

Question
The functions u(x) u(x) and v(x) v(x) are differentiable. \newlineThe function w(x) w(x) is defined as: w(x)=u(x)v(x) w(x)= \frac{u(x)}{v(x)} \newlineIf u(5)=3 u(5)= 3 , u′(5)=−2 u'(5)= -2 , v(5)=7 v(5)= 7 , and v′(5)=1 v'(5)= 1 , what is w′(5) w'(5) ? \newlineSimplify any fractions. \newlinew′(5)= w'(5)= _____
Get tutor helpright-arrow

Posted 9 months ago

Question
The functions a(x) a(x) and b(x) b(x) are differentiable. \newlineThe function c(x) c(x) is defined as: c(x)=a(x)b(x) c(x)= \frac{a(x)}{b(x)} \newlineIf a(2)=4 a(2)= 4 , a′(2)=5 a'(2)= 5 , b(2)=1 b(2)= 1 , and b′(2)=−3 b'(2)= -3 , what is c′(2) c'(2) ? \newlineSimplify any fractions. \newlinec′(2)= c'(2)= _____
Get tutor helpright-arrow

Posted 9 months ago

Question
The functions m(x) m(x) and n(x) n(x) are differentiable. \newlineThe function o(x) o(x) is defined as: o(x)=m(x)n(x) o(x)= \frac{m(x)}{n(x)} \newlineIf m(7)=2 m(7)= 2 , m′(7)=−1 m'(7)= -1 , n(7)=4 n(7)= 4 , and n′(7)=8 n'(7)= 8 , what is o′(7) o'(7) ? \newlineSimplify any fractions. \newlineo′(7)= o'(7)= _____
Get tutor helpright-arrow

Posted 9 months ago

View all (100)

Related topics

Algebra - Order of OperationsAlgebra - Distributive Property`X` and `Y` AxesGeometry - Scalene TriangleCommon MultipleGeometry - Quadrant