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

Question

asked Nov 5, 2023 209k views

1 Answer

Hemant Sharma · Answer 1 · 2023-11-09T07:55:26+0000

Step-by-step explanation:

First we divide both sides by 4:

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

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:

$x=(\log (28.75))/(\log (8))=1.61516335$

Answer:

Rounded to two decimal places: x = 1.62