4^x=9... solve for x?

Question

solve:
4^x=9

please show me how u work it out

Answer 1

hmm..it seems to involve logarithms.
taking the logarithm of both sides, we have:
log 4^x = log 9.
Recall the property that
log a^n = nloga,
log4^x = xlog 4. So,
xlog4 = log 9
x = log9/log4.
remember that
log4 = log2^2 = 2log 2 and
log 9 = log3^2 = 2log3
so, log9/log4 = log3/log2.

recall the base conversion formula: log b a where b is the base = log a/ log b.
so, x = log of 3 base 2.

hope its clear enough! have a good day:D

Answer 2

4^x = 9
2^2x =9
take the sqaure off both sides
2x =square root of 9
2x = 3.
x =3/2
=1.5

Answer 3

4^x=9
log(4^x) = log(9)
x*log(4) = log(9)
x = log(9)/log(4)
x = 1.58496

edit: i'll explain the steps
1. you have to log both sides
2. you have to use the log rule: log(x^b) = b*log(x)
3. divide

Answer 4

log 4 * x = log 9
x = log 9/log 4

I think...