log15(1) = x

1 = 15^x

Since we can say that 15^0 = 1, we can rewrite the problem as:

15^0 = 15^x

(Note that 15^0 replaced 1 in the problem 1 = 15^x, becoming 15^0 = 15^x.)

Therefore, x = 0.

Is this 10^(3x) = 55 or 10^(3) * x = 55? The notation you used was a bit unclear. But I'm going to assume you mean 10^(3x) = 55.2) "10^3x = 55"

I did:

10^3x = 55^1

3x = 55

x = 18.333 ---> I attempted to correct this and came up with x = log(10)55/3. I still resulted with x = 18.333 and I don't understand why this was still marked wrong.

Thanks in advance.

From this, you CANNOT say that 3x = 55. You can't set the exponent of the left hand side equal to the base of the right hand side (doing so is invalid and makes no sense). However, we can solve for x by taking the log of both sides:

log(10^(3x)) = log(55)

3x*log(10) = log(55)

3x = log(55)

x = log(55)/3

This will be an irrational answer that you'll have to plug into your calculator to find.