Question

What is the solution to 4^(log4(x+8))=4^2

x=-8
x=-4
x=4
x=8

Answer 1

Hi there! The answer is x = 8.


`{4}^{ log_(4)(x + 8) } = {4}^(2)`
Let's solve this equation step by step!


First we use the following rule.

`{g}^(a) = {g}^(b) \\ a = b`
which basically means that an exponential equation with the same base on both sides of the equation must also have the same exponents.

We get the following.

`log_(4)(x + 8) = 2`

Now we use the following rule for logarithms.

`log_(a)(x) = b \\ x = {a}^(b)`

When we apply this rule in our eqiation, we end up with the following.

`x + 8 = {4}^(2)`

Now we only need to do some basic math, work out the exponents first.

`x + 8 = 16`

Subtract 8.

`x = 8`

~ Hope this helps you!

Answer 2

x=8

Explanation:

Use the main property of logarithms:

`a^(\log_ab)=b.`

Then
`4^(\log_4(x+8))=x+8.`

Now the equation takes look

`x+8=4^2,\\ \\x+8=16,\\ \\x=16-8,\\ \\x=8.`

Check whether x=8 is the solution:

`4^(\log_4(8+8))=4^(\log_416)=4^(\log_44^2)=4^(2\log_44)=4^(2\cdot 1)=4^2=16.`