Question

Write the given equation in exponential form.



log7 = -6

Answer 1

`10^(-6)=7`

Explanation:

Remember that according to the laws of logarithms if
`log_ay=x`, then
`a^x=y`,

In other words to convert a logarithm to an exponential equation we just need to raise the base of the logarithm to the result and equate that to the argument of the logarithm.

Since our logarithm does not have a base, its base is 10; therefore
`a=10`. The argument of our logarithm is 7, so
`y=7`. The result of our logarithm is -6, so
`x=-6`.

Replacing values

`log_ay=x` ⇔
`a^x=y`

`log_(10)7=-6` ⇔
`10^(-6)=7`

By the way
`log_(10)7=-6` is not a true equation since
`10^(-6)\\eq 7`.