Solve the exponential equation for x. 49^(-x-7)*7^(4x+8)=49^(5x-3) x=

Understanding the relationship: Understand the relationship between the bases of the exponents. Since 49 is 7 squared (7^2), we can rewrite the equation with a common base.Rewriting 49 as 7^2: Rewrite 49 as 7^2 in the equation. (7^2)^(-x-7) * 7^(4x+8) = (7^2)^(5x-3)Applying the power of a power rule: Apply the power of a power rule to simplify the exponents. 7^(2*(-x-7)) * 7^(4x+8) = 7^(2*(5x-3))Multiplying the exponents: Multiply the exponents inside the parentheses. 7^(-2x-14) * 7^(4x+8) = 7^(10x-6)Setting the exponents equal: Since the bases are the same, we can set the exponents equal to each other. -2x - 14 + 4x + 8 = 10x - 6Combining like terms: Combine like terms. 2x - 6 = 10x - 6Subtracting 2x from both sides: Subtract 2x from both sides to get all x terms on one side. -6 = 8x - 6Adding 6 to both sides: Add 6 to both sides to isolate the x term. 0 = 8xDividing both sides by 8: Divide both sides by 8 to solve for x. x = 0 / 8Simplifying the fraction: Simplify the fraction to find the value of x. x = 0

Resources

Testimonials

Plans

Resources

Testimonials

Plans

AI tutor

Welcome to Bytelearn!

Let’s check out your problem:

Solve the exponential equation for
x.

49^(-x-7)*7^(4x+8)=49^(5x-3)

x=

Solve the exponential equation for $x$ . $\newline$ $49^{-x-7} \cdot 7^{4 x+8}=49^{5 x-3}$ $\newline$ $x=$

View step-by-step help

Home

Math Problems

Algebra 2

Composition of linear and quadratic functions: find a value

Full solution

Q. Solve the exponential equation for

x

\newline

49^{-x-7} \cdot 7^{4 x+8}=49^{5 x-3}

\newline

x=

Understanding the relationship: Understand the relationship between the bases of the exponents. $\newline$ Since $49$ is $7$ squared ( $7^2$ ), we can rewrite the equation with a common base.
Rewriting $49$ as $7^2$ : Rewrite $49$ as $7^2$ in the equation. $\newline$ $(7^2)^{(-x-7)} \times 7^{(4x+8)} = (7^2)^{(5x-3)}$
Applying the power of a power rule: Apply the power of a power rule to simplify the exponents. $7^{2(-x-7)} \times 7^{4x+8} = 7^{2(5x-3)}$
Multiplying the exponents: Multiply the exponents inside the parentheses. $\newline$ $7^{(-2x-14)} \times 7^{(4x+8)} = 7^{(10x-6)}$
Setting the exponents equal: Since the bases are the same, we can set the exponents equal to each other. $\newline$ $-2x - 14 + 4x + 8 = 10x - 6$
Combining like terms: Combine like terms. $2x - 6 = 10x - 6$
Subtracting $2x$ from both sides: Subtract $2x$ from both sides to get all $x$ terms on one side. $\newline$ $-6 = 8x - 6$
Adding $6$ to both sides: Add $6$ to both sides to isolate the $x$ term. $\newline$ $0 = 8x$
Dividing both sides by $8$ : Divide both sides by $8$ to solve for $x$ . $x = \frac{0}{8}$
Simplifying the fraction: Simplify the fraction to find the value of $x$ . $x = 0$