4^4x=8 find x

Question

4^4x=8 find x

zepdrix · Answer

$$\large\rm 4^{4x}=8$$The x is in the denominator like this?

zepdrix · Answer

I suppose we could apply natural log to each side,
then we'll be able to use a log rule to remove the x from the exponent position.

zepdrix · Answer

$$\large\rm \ln(4^{4x})=\ln8$$

zepdrix · Answer

Recall your log exponent rule,$$\large\rm \color{orangered}{\ln(a^b)=b\cdot \log(a)}$$

zepdrix · Answer

That allows us to bring the 4x out of the exponent position,$$\large\rm 4x\cdot \ln4=\ln8$$

zepdrix · Answer

From that point, solve for x, k? :)
@lexiquesse

lexiquesse · Answer

sorry, i was working on a different problem, but is it 1/2? @zepdrix

ganeshie8 · Answer

Nope

lexiquesse · Answer

oops i meant 1 and 1/2

zepdrix · Answer

I don't understand.
Are you just guessing? :o

Do you understand how to solve for x?

lexiquesse · Answer

.375? no im not, i took ln(8)/ln(4) and got 1.5, and 1.5/4=.375

ganeshie8 · Answer

4^4x =  8

Notice that both 4 and 8 are powers of 2 :

(2^2)^4x = 2^3

2^8x = 2^3

lexiquesse · Answer

im very confused

zepdrix · Answer

.375, yayy good job \c:/

Ahh I forgot we could simply do the exponent method for this one,
doh!

lexiquesse · Answer

its okay:p