If 36 = 6 × 6 = 62, then 1 expressed as a power with the base 6 is ________.

Question

asked Sep 7, 2024 58.6k views

1 Answer

Amer Al Zibak · Answer 1 · 2024-09-12T17:57:06+0000

To express 1 as a power with the base 6, we can use logarithms.

We have the equation:

36 = 6^2

Taking the logarithm base 6 of both sides:

$\log_6(36) = \log_6(6^2)$

Applying the logarithmic property, we can bring down the exponent:

$\log_6(36) = 2\log_6(6)$

Since
$\log_b(b) = 1$ , where b is the base of the logarithm, we have:

$\log_6(36) = 2 * 1$

Simplifying the expression:

$\log_6(36) = 2$

Therefore, 1 expressed as a power with the base 6 is
6^0 .