Question

solve for x, rounding to the nearest hundredth. 10^x = 45

Explanation:

Step1: Take log base 10 of both sides

To solve for \( x \) in the equation \( 10^x = 45 \), we can take the common logarithm (log base 10) of both sides. By the property of logarithms, \( \log_{10}(10^x) = x \), so we have:
\[
\log_{10}(10^x) = \log_{10}(45)
\]
Simplifying the left side gives:
\[
x = \log_{10}(45)
\]

Step2: Calculate the logarithm

Using a calculator, we find that \( \log_{10}(45) \approx 1.653212513775343 \).

Step3: Round to the nearest hundredth

Rounding \( 1.653212513775343 \) to the nearest hundredth (two decimal places), we look at the third decimal place, which is 3. Since 3 is less than 5, we round down. So, \( 1.653212513775343 \approx 1.65 \).

Answer:

\( x \approx 1.65 \)