Solve. Round your answer to the nearest thousandth. 9^x = 7 x = ____

Take Logarithm: We need to solve the equation 9^x = 7 for x. To do this, we will take the logarithm of both sides of the equation. log(9^x) = log(7)Simplify Left Side: Using the power property of logarithms, which states that log_b(M^n) = n*log_b(M), we can simplify the left side of the equation. x*log(9) = log(7)Isolate x: Now we will isolate x by dividing both sides of the equation by log(9). x = log(7) / log(9)Calculate x: We will now calculate the value of x using a calculator. x ≈ log(7) / log(9) x ≈ 0.8450980400142568 / 0.9542425094393249 x ≈ 0.885

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. $\newline$ $9^x = 7$ $\newline$ $x =$ ____

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

9^x = 7

\newline

x =

____

Take Logarithm: We need to solve the equation $9^x = 7$ for $x$ . To do this, we will take the logarithm of both sides of the equation. $\newline$ $\log(9^x) = \log(7)$
Simplify Left Side: Using the power property of logarithms, which states that $\log_b(M^n) = n\log_b(M)$ , we can simplify the left side of the equation. $\newline$ $x\log(9) = \log(7)$
Isolate $x$ : Now we will isolate $x$ by dividing both sides of the equation by $\log(9)$ . $\newline$ $x = \frac{\log(7)}{\log(9)}$
Calculate x: We will now calculate the value of $x$ using a calculator. $x \approx \frac{\log(7)}{\log(9)}$ $x \approx \frac{0.8450980400142568}{0.9542425094393249}$ $x \approx 0.885$