Question

How do you solve `4^x= 7`?

Answer 1

I found: `x=1.4036`

Explanation:

If you can use a pocket calculator (or tables) you could change it into a log using the definition of logarithm:
`log_ab=x->a^x=b`
where in your case you get:
`log_4(7)=x`
you can now change base of your log to evaluate it using a pocket calculator (for example, using the base `e` of the natural logarithm, `ln`):
`x=log_4(7)=(ln(7))/(ln(4))=1.4036`