ANSWER
[tex]A.\text{ }0.48[/tex]
EXPLANATION
We want to solve for x in the equation:
[tex]4*2^{5x}=21[/tex]
First, divide both sides of the equation by 4:
[tex]\begin{gathered} \frac{4*2^{5x}}{4}=\frac{21}{4} \\ \\ 2^{5x}=5.25 \end{gathered}[/tex]
Find the logarithm of both sides of the equation:
[tex]\log2^{5x}=\log5.25[/tex]
Simplify the left-hand side of the equation:
[tex]5x(\log2)=\log5.25[/tex]
Divide both sides by log2:
[tex]5x=\frac{\log5.25}{\log2}=2.392[/tex]
Divide both sides of the equation by 5:
[tex]\begin{gathered} \frac{5x}{5}=\frac{2.392}{5} \\ \\ x=0.48 \end{gathered}[/tex]
The answer is option A.
