Question

now you try this! click to check your work and answer! 40 = 2(5^x) click the button to see the steps to solving! solve for x. use the pencil tool to do your work here. 40 = 2(5)^x

Explanation:

Step1: Isolate the exponential term

Divide both sides by 2.
$\frac{40}{2}=\frac{2(5^{x})}{2}$
$20 = 5^{x}$

Step2: Take the logarithm of both sides

Use the common - logarithm (base 10). $\log(20)=\log(5^{x})$

Step3: Apply the power - rule of logarithms

$\log(20)=x\log(5)$

Step4: Solve for x

$x = \frac{\log(20)}{\log(5)}$
Using a calculator, $\log(20)\approx1.3010$ and $\log(5)\approx0.69897$.
$x=\frac{1.3010}{0.69897}\approx1.86$

Answer:

$x\approx1.86$