Question

Write the log equation as an exponential equation

Answer 1

Given:

The equation is:

$\log_{(x-2)}(x^2-4x-6)=\dfrac{4}{5}$

To find:

The exponential equation of the given logarithmic equation.

Solution:

We have,

$\log_{(x-2)}(x^2-4x-6)=\dfrac{4}{5}$

According to property of logarithm,

$\log_ax=b\Leftrightarrow x=a^b$

Using the property of logarithm, we get

$x^2-4x-6=(x-2)^{\frac{4}{5}}$

Therefore, the required exponential equation is $x^2-4x-6=(x-2)^{\frac{4}{5}}$.