Question

Solve 3^x=5. What are the exact and approximate solutions?

Answer 1

The answer is

1.46

Explanation:

`{3}^(x) = 5`

Take logarithm of both sides of the equation

That's

`log(3)^(x) = log(5)`

Using the rules of logarithms

`log(3)^(x) = x log(3)`

So we have

`xlog(3) = log(5)`

Divide both sides by log 3

We have

`x = ( log(5) )/( log(3) )`

We have the final answer as

1.46497

which is

1.46 to 2 decimal places

Hope this helps you