Question

1.2^a x 2^5 =2^0

a=?

Answer 1

One thing that is unclear here is whether the "1." at the start is part of the number "1.2" or if it is an enumeration of the question, and the base raised to the exponent is in fact 2.

The rest of the equation seems to indicate the latter, so we'll solve both:

If 1.2ᵃ ₓ 2⁵ = 2⁰, then a is approximately equal to -19.009.

If as I'm guessing is the correct question, 2ᵃ ₓ 2⁵ = 2⁰, then a is equal to -5.

Explanation:

Interpretation #1:

`1.2^a * 2^5 = 2^0\\1.2^a * 32 = 1\\1.2^a = (1)/(32)\\log_(1.2) (1)/(32) = a\\a \approx -19.009`

Interpretation #2:

Here the question is much simpler, as we need only add the exponents when adding and dividing:

`2^a * 2^5 = 2^0\\2^a = 2^0 /2^5\\2^a = 2^(-5)\\a = -5`