100*2^(4x)=15 What is the solution of the equation? Round your answer, if necessary, to the nearest thousandth. x~~

Isolate exponential term: First, we need to isolate the exponential term by dividing both sides of the equation by 100. 100*2^(4x) = 15 2^(4x) = 15 / 100 2^(4x) = 0.15Apply logarithm: Now, we apply the logarithm to both sides of the equation to solve for x. We can use the natural logarithm (ln) or the common logarithm (log). Here, we'll use the natural logarithm for convenience. ln(2^(4x)) = ln(0.15)Move exponent in front: Using the power property of logarithms, we can move the exponent in front of the logarithm. 4x * ln(2) = ln(0.15)Solve for x: Next, we solve for x by dividing both sides of the equation by 4*ln(2). x = ln(0.15) / (4 * ln(2))Calculate x: Now, we calculate the value of x using a calculator. x ≈ ln(0.15) / (4 * ln(2)) x ≈ -1.897119984 / (4 * 0.693147181) x ≈ -1.897119984 / 2.772588724 x ≈ -0.684

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100*2^(4x)=15
What is the solution of the equation?
Round your answer, if necessary, to the nearest thousandth.

x~~

$100 \cdot 2^{4 x}=15$ $\newline$ What is the solution of the equation? $\newline$ Round your answer, if necessary, to the nearest thousandth. $\newline$ $x \approx$

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Precalculus

Solve exponential equations using logarithms

Full solution

100 \cdot 2^{4 x}=15

\newline

What is the solution of the equation?

\newline

Round your answer, if necessary, to the nearest thousandth.

\newline

x \approx

Isolate exponential term: First, we need to isolate the exponential term by dividing both sides of the equation by $100$ . $\newline$ $100 \cdot 2^{4x} = 15$ $\newline$ $2^{4x} = \frac{15}{100}$ $\newline$ $2^{4x} = 0.15$
Apply logarithm: Now, we apply the logarithm to both sides of the equation to solve for $x$ . We can use the natural logarithm ( $\ln$ ) or the common logarithm ( $\log$ ). Here, we'll use the natural logarithm for convenience. $\newline$ $\ln(2^{4x}) = \ln(0.15)$
Move exponent in front: Using the power property of logarithms, we can move the exponent in front of the logarithm. $4x \cdot \ln(2) = \ln(0.15)$
Solve for x: Next, we solve for $x$ by dividing both sides of the equation by $4\cdot\ln(2)$ .
$x = \frac{\ln(0.15)}{4 \cdot \ln(2)}$
Calculate x: Now, we calculate the value of x using a calculator. $\newline$ $x \approx \frac{\ln(0.15)}{4 \cdot \ln(2)}$ $\newline$ $x \approx \frac{-1.897119984}{4 \cdot 0.693147181}$ $\newline$ $x \approx \frac{-1.897119984}{2.772588724}$ $\newline$ $x \approx -0.684$