To solve the equation [tex]\( 10 \cdot \log(4x) = 25 \)[/tex], follow these steps:
1. Isolate the logarithmic expression.
[tex]\[
10 \cdot \log(4x) = 25
\][/tex]
Divide both sides by 10:
[tex]\[
\log(4x) = \frac{25}{10} = 2.5
\][/tex]
2. Rewrite the equation in exponential form.
The equation [tex]\(\log(4x) = 2.5\)[/tex] can be written in exponential form as:
[tex]\[
4x = 10^{2.5}
\][/tex]
3. Calculate the numeric value of [tex]\(10^{2.5}\)[/tex].
[tex]\(10^{2.5}\)[/tex] approximately equals 316.23.
4. Solve for [tex]\(x\)[/tex].
Divide both sides of the equation [tex]\(4x = 316.23\)[/tex] by 4:
[tex]\[
x = \frac{316.23}{4} \approx 79.06
\][/tex]
Hence, the solution to the equation [tex]\(10 \cdot \log(4x) = 25\)[/tex] rounded to two decimal places is:
[tex]\[
\boxed{x = 79.06}
\][/tex]
Therefore, the correct answer is:
B. [tex]\( x = 79.06 \)[/tex]
