To solve the equation [tex]\(5^x = 26\)[/tex], we'll need to use logarithms. Here is a step-by-step approach:
1. Take the Logarithm of Both Sides: Applying the logarithm on both sides of the equation helps us handle the exponent.
[tex]\[
\log(5^x) = \log(26)
\][/tex]
2. Apply Logarithm Properties: Utilize the property of logarithms that allows us to bring the exponent in front of the log function:
[tex]\[
x \cdot \log(5) = \log(26)
\][/tex]
3. Solve for [tex]\(x\)[/tex]: To isolate [tex]\(x\)[/tex], we divide both sides by [tex]\(\log(5)\)[/tex]:
[tex]\[
x = \frac{\log(26)}{\log(5)}
\][/tex]
4. Calculate the Logarithms:
- Calculate [tex]\(\log(26)\)[/tex]
- Calculate [tex]\(\log(5)\)[/tex]
5. Divide the Results:
[tex]\[
x = \frac{\log(26)}{\log(5)}
\][/tex]
6. Round to Two Decimal Places:
[tex]\[
x \approx 2.02
\][/tex]
Therefore, the solution to the equation [tex]\(5^x = 26\)[/tex], rounded to two decimal places, is:
[tex]\[
\boxed{x = 2.02}
\][/tex]
Hence, the correct answer is:
B. [tex]\(x = 2.02\)[/tex]
