Question

Question 5 Solve correct to 2 decimal places. a 4(8)*= 115

Answer 1

Explanation:

$4(8)^x=115$

First we divide both sides by 4:

$\begin{gathered} \frac{4(8)^x}{4}=\frac{115}{4} \\ 8^x=28.75 \end{gathered}$

Now we have to take logarithm on both sides:

$\log (8^x)=\log (28.75)$

Using the logarithm of a power rule:

$\log (a^b)=b\log (a)$

we have:

$x\log (8)=\log (28.75)$

Now, clearing x:

$x=\frac{\log (28.75)}{\log (8)}=1.61516335$

Answer:

Rounded to two decimal places: x = 1.62