Question

what exponent would make the two expressions equivalent: (3^(3)^(x)=3^(24)

Answer 1

[AI-generated answer — Bot GPT 3.5]

To make the two expressions equivalent, we need to find the value of x that makes the exponents equal.

We have:

3^(3^x) = 3^24

Since the bases are the same (3), we can set the exponents equal to each other:

3^x = 24

To solve for x, we can take the logarithm of both sides of the equation:

log base 3 of (3^x) = log base 3 of 24

x = log base 3 of 24

Using a calculator, we can find that log base 3 of 24 is approximately 2.3802.

Therefore, the exponent that would make the two expressions equivalent is x ≈ 2.3802.