4^x=10^4 What does 8^x equal?

Question

Please explain.

Answer 1

Hey there!

Nice problem.

Well. Change the problem from 4^x=10^4 into 2^2x=10^4, since 2^2x=4^x.

Then, the following are true:

2^2x=10^4 -->
(2^x)^2=10^4 -->
2^x=10^2 -->
(2^x)^3=(10^2)^3 -->
2^3x=10^6 -->
8^x=10^6

So 8^x=10^6.

Hope it helps!

Answer 2

4^x = 10^4
(2^2)^x = 10^4
2^(2*x) = 10^4
(2^x)^2 = 10^4
Take square root of both sides:
2^x = 10^2
Cube both sides:
(2^x)^3 = (10^2)^3
2^(3x) = 10^(2*3) = 10^6
(2^3)^x = 10^6
8^x = 10^6

I used the fact that (a^b)^c = a^(b*c) several times