Question

What is 5^x = 79

Using logarithmic notation to represent the solution to each of the following equations

Answer 1

`x = log_(5)(79)`

Explanation:

5^x = 79 can be solved using logarithms. using the properties:

`a = b \implies log(a) = log(b)`

and

`log( {a}^(x) ) = x log(a)`

and

`log_(a)( {a}^(x) ) = x`

first, we take the logarithm of both sides, base 5.

`log_(5)( {5}^(x) ) = log_(5)(79)`

then, use property 2:

`x log_(5)(5) = log_(5)(79)`

and property 3:

`x = log_(5)(79)`

thus, we have our solution.