Question

State the solution in terms of x 4^x+6 = 20

Answer 1

We have the question as

`4^(x+6)=20`

Let us introduce logarithms to base 4 to both sides of the equation:

`\log _44^(x+6)=\log _420`

Applying the law of logarithm that states

`\log A^B=B\log A`

we have

`(x+6)\log _44=\log _420`

Applying the law that states

`\log _nn=1`

we have

`\begin{gathered} (x+6)*1=\log _420 \\ x+6=\log _420 \end{gathered}`

Collecting like terms, we have

`x=-6+\log _420`

Therefore, the answer is OPTION C.