Solve. Round your answer to the nearest thousandth. 7^x = 2 x = ____

Write Equation: Write down the equation. We are given the equation 7^x = 2. We need to solve for x.Apply Logarithm: Apply the logarithm to both sides of the equation. To solve for x, we can use logarithms. Applying the natural logarithm (ln) to both sides gives us ln(7^x) = ln(2).Use Power Property: Use the power property of logarithms. The power property of logarithms states that ln(a^b) = b*ln(a). We apply this property to simplify the left side of the equation: x*ln(7) = ln(2).Isolate x: Isolate x. To solve for x, we divide both sides of the equation by ln(7): x = ln(2)/ln(7).Calculate Value: Calculate the value of x. Using a calculator, we find the values of ln(2) and ln(7) and then divide them to find x. x = ln(2)/ln(7) ≈ 0.69314718/1.94591015 ≈ 0.356207187Round Answer: Round the answer to the nearest thousandth. Rounding the value of x to the nearest thousandth gives us x ≈ 0.356.

Resources

Testimonials

Plans

Resources

Testimonials

Plans

AI tutor

Welcome to Bytelearn!

Let’s check out your problem:

Solve. Round your answer to the nearest thousandth. $\newline$ $7^x = 2$ $\newline$ $x =$ __

View step-by-step help

Home

Math Problems

Algebra 2

Solve exponential equations using common logarithms

Full solution

Q. Solve. Round your answer to the nearest thousandth.

\newline

7^x = 2

\newline

x =

Write Equation: Write down the equation. $\newline$ We are given the equation $7^x = 2$ . We need to solve for $x$ .
Apply Logarithm: Apply the logarithm to both sides of the equation. $\newline$ To solve for $x$ , we can use logarithms. Applying the natural logarithm ( $\ln$ ) to both sides gives us $\ln(7^x) = \ln(2)$ .
Use Power Property: Use the power property of logarithms. The power property of logarithms states that $\ln(a^b) = b\cdot\ln(a)$ . We apply this property to simplify the left side of the equation: $x\cdot\ln(7) = \ln(2)$ .
Isolate x: Isolate $x$ . $\newline$ To solve for $x$ , we divide both sides of the equation by $\ln(7)$ : $x = \frac{\ln(2)}{\ln(7)}$ .
Calculate Value: Calculate the value of $x$ . Using a calculator, we find the values of $\ln(2)$ and $\ln(7)$ and then divide them to find $x$ . $x = \frac{\ln(2)}{\ln(7)} \approx \frac{0.69314718}{1.94591015} \approx 0.356207187$
Round Answer: Round the answer to the nearest thousandth. $\newline$ Rounding the value of $x$ to the nearest thousandth gives us $x \approx 0.356$ .