Question
solve for x rounding to nearest hundreth
3^x=80
3^x=80
Answers
GPT-4o mini
To solve the equation \(3^x = 80\) for \(x\), we can take the logarithm of both sides. Using logarithm properties, we have:
\[
x \cdot \log(3) = \log(80)
\]
Now, we can solve for \(x\):
\[
x = \frac{\log(80)}{\log(3)}
\]
Using a calculator to find \(\log(80)\) and \(\log(3)\):
\[
\log(80) \approx 1.9031
\]
\[
\log(3) \approx 0.4771
\]
Now, substitute these values into the equation:
\[
x \approx \frac{1.9031}{0.4771} \approx 3.98
\]
Rounding to the nearest hundredth, we find:
\[
\boxed{3.98}
\]
\[
x \cdot \log(3) = \log(80)
\]
Now, we can solve for \(x\):
\[
x = \frac{\log(80)}{\log(3)}
\]
Using a calculator to find \(\log(80)\) and \(\log(3)\):
\[
\log(80) \approx 1.9031
\]
\[
\log(3) \approx 0.4771
\]
Now, substitute these values into the equation:
\[
x \approx \frac{1.9031}{0.4771} \approx 3.98
\]
Rounding to the nearest hundredth, we find:
\[
\boxed{3.98}
\]