Question

Write the log equation as an exponential equation

Answer 1

Given:

The equation is:

`\log_((x-2))(x^2-4x-6)=(4)/(5)`

To find:

The exponential equation of the given logarithmic equation.

Solution:

We have,

`\log_((x-2))(x^2-4x-6)=(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)^{(4)/(5)}`

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