solve 2^x=8

Think of how many times 2 needs to be multiplied in order to get eight.

2 x 2 = 4

4 x 2 = 8

Therefore, since 3 '2's were used, x = 3

2^3 = 8. x is equal to 3

1. $$2^x=8\quad|\quad \ln{}$$
2. $$\ln{(2^x)}=\ln(8)$$
3. $$x*\ln{2}=\ln{8}$$
4. $$x=\frac{\ln{8}}{\ln{2}}=\frac{\ln{(2*2*2)}}{\ln{2}}=\frac{\ln{2}+\ln{2}+\ln{2}}{\ln{2}}=\frac{\ln{2}}{\ln{2}}+\frac{\ln{2}}{\ln{2}}+\frac{\ln{2}}{\ln{2}}=1+1+1=3$$
5. $$\boxed{x=3}$$

S.

We can also equate bases to solve this.

2^x = 8

2^x = 2³

So, x = 3.