Given:
The equation is:
[tex]\log_{(x-2)}(x^2-4x-6)=\dfrac{4}{5}[/tex]
To find:
The exponential equation of the given logarithmic equation.
Solution:
We have,
[tex]\log_{(x-2)}(x^2-4x-6)=\dfrac{4}{5}[/tex]
According to property of logarithm,
[tex]\log_ax=b\Leftrightarrow x=a^b[/tex]
Using the property of logarithm, we get
[tex]x^2-4x-6=(x-2)^{\frac{4}{5}}[/tex]
Therefore, the required exponential equation is [tex]x^2-4x-6=(x-2)^{\frac{4}{5}}[/tex].
