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Tamiku [17]
3 years ago
12

Inverse of y equals 12 to the x

Mathematics
1 answer:
e-lub [12.9K]3 years ago
5 0

Answer:

f^{-1}(x) = log_{12}(y)

Step-by-step explanation:

We have the following function

y = 12^x, and we need to find the inverse function.

To find the inverse function we should solve the equation for "x". To do so, first, we need to:

1. Take the logarithm in both sides of the equation:

lg_12 (y) = log _12 (12^x)

(Please read lg_12 as: "Logarithm with base 12")

From property of logarithm, we know that lg (a^b) = b*log(a)

Then:

lg_12 (y) = x*log _12 (12)

We also know that log _12 (12) = 1

Then:

x = log_12(y).

Then, the inverse of: y= 12^x is:

f^{-1}(x) = log_{12}(y)

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