Question

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

Answer 1

Step-by-step explanation:

`4(8)^x=115`

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