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. {:[32^((x)/(5))=((1)/(16))^(4x-3)],[x=]:}

Solve the exponential equation for x x .\newline32x5=(116)4x−3x= \begin{array}{l} 32^{\frac{x}{5}}=\left(\frac{1}{16}\right)^{4 x-3} \\ x= \end{array}

View step-by-step helpView step-by-step help
Homeright chevron icon
Math Problemsright chevron icon
Calculusright chevron icon
Find derivatives of sine and cosine functionsright chevron icon

Full solution

Q. Solve the exponential equation for x x .\newline32x5=(116)4x−3x= \begin{array}{l} 32^{\frac{x}{5}}=\left(\frac{1}{16}\right)^{4 x-3} \\ x= \end{array}
  1. Recognize Powers of 22: Recognize that 3232 and 1/161/16 can be written as powers of 22. 32=2532 = 2^5 and 1/16=2−41/16 = 2^{-4}. Rewrite the equation using these powers of 22. (25)x/5=(2−4)4x−3(2^5)^{x/5} = (2^{-4})^{4x-3}
  2. Apply Power Rule: Apply the power of a power rule to simplify both sides of the equation.\newline(25∗(x5))=(2−4∗(4x−3))(2^{5*(\frac{x}{5})}) = (2^{-4*(4x-3)})\newline2x=2−16x+122^x = 2^{-16x+12}
  3. Set Exponents Equal: Since the bases are the same, set the exponents equal to each other. x=−16x+12x = -16x + 12
  4. Solve for x: Solve for x by adding 16x16x to both sides of the equation.\newlinex+16x=12x + 16x = 12\newline17x=1217x = 12
  5. Isolate xx: Divide both sides by 1717 to isolate xx.x=1217x = \frac{12}{17}

More problems from Find derivatives of sine and cosine functions

Question
Find the derivative of f(x) f(x) .\newlinef(x)=cos⁡(x) f(x) = \cos(x) \newlinef′(x)= f'(x) = ______
Get tutor helpright-arrow

Posted 7 months ago

Question
Find the derivative of f(x) f(x) .\newlinef(x)=tan⁡(x) f(x) = \tan(x) \newlinef′(x)= f'(x) = ______
Get tutor helpright-arrow

Posted 9 months ago

Question
Find the derivative of f(x) f(x) .\newlinef(x)=ex f(x) = e^x \newlinef′(x)= f'\left(x\right) = ______
Get tutor helpright-arrow

Posted 9 months ago

Question
Find the derivative of f(x) f(x) .\newlinef(x)=ln⁡(x) f(x) = \ln(x) \newlinef′(x)= f'(x) = ______
Get tutor helpright-arrow

Posted 9 months ago

Question
Find the derivative of f(x) f(x) .\newlinef(x)=tan⁡−1x f(x) = \tan^{-1}{x} \newlinef′(x)= f'(x) = ______
Get tutor helpright-arrow

Posted 9 months ago

Question
Find the derivative of f(x) f(x) .\newlinef(x)=xex f(x) = x e^x \newlinef′(x)= f'\left(x\right) = ______
Get tutor helpright-arrow

Posted 9 months ago

Question
Find the derivative of f(x) f(x) . \newlinef(x)=exx f(x) = \frac{e^x}{x} \newlinef′(x)= f'(x) = ______
Get tutor helpright-arrow

Posted 9 months ago

Question
Find the derivative of f(x) f(x) . \newline f(x)=e(x+1) f(x) = e^{(x + 1)} \newline f′(x)= f'\left(x\right) = ______
Get tutor helpright-arrow

Posted 7 months ago

Question
Find the derivative of f(x) f(x) . \newlinef(x)=x+3 f(x) = \sqrt{x+3} \newlinef′(x)= f'(x) = ______
Get tutor helpright-arrow

Posted 9 months ago

Question
Find the derivative of g(x) g(x). \newline g(x)=ln⁡(2x) g(x) = \ln(2x) \newline g′(x)= g^{\prime}(x) = ______
Get tutor helpright-arrow

Posted 10 months ago

View all (129)

Related topics

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