Explanation:
[tex]4(8)^x=115[/tex]
First we divide both sides by 4:
[tex]\begin{gathered} \frac{4(8)^x}{4}=\frac{115}{4} \\ 8^x=28.75 \end{gathered}[/tex]
Now we have to take logarithm on both sides:
[tex]\log (8^x)=\log (28.75)[/tex]
Using the logarithm of a power rule:
[tex]\log (a^b)=b\log (a)[/tex]
we have:
[tex]x\log (8)=\log (28.75)[/tex]
Now, clearing x:
[tex]x=\frac{\log (28.75)}{\log (8)}=1.61516335[/tex]
Answer:
Rounded to two decimal places: x = 1.62
