# Solve for $x$.

$
2^{x+5}=13^{2 x}
$

Write the exact answer using either base-10 or base-e logarithms.

Question

# Solve for $x$.

$
2^{x+5}=13^{2 x}
$

Write the exact answer using either base-10 or base-e logarithms.

StudyXY · Accepted Answer

: To solve the equation, we will take the base-10 logarithm (log) of both sides. : Using the power rule for logarithms, which states that $\log(a^b) = b\log(a)$, we can rewrite the equation as: : Next, we will isolate the term with $x$ on one side of the equation. : Now, we can simplify the equation further by bringing all terms involving $x$ to the left side and constants to the right side. : Factor out $x$ from the left side of the equation. : Solve for $x$ by dividing both sides by the expression in parentheses. : Simplify the equation by calculating the value of the logarithm and performing the division. The solution to the equation $2^{x+5} = 13^{2x}$ is approximately $x \approx -5.83$.

Q
QuestionAnatomy and Physiology

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Full Solution Locked

Step 1
: To solve the equation, we will take the base- 10 logarithm (log) of both sides.

Step 2
: Using the power rule for logarithms, which states that 1$, we can rewrite the equation as:

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