Question

5^x=62 Giving 20 points!

Algebra 2, Chapter 6-7. Common Logarithms.
The answer key says its 2.5, but I need some help to understand how to get that answer by showing work.

Answer 1

2.5

Explanation:

ln(5^x)=ln(62)

`x=(ln62)/(ln5)`

≈2.56433

Answer 2

x = 2.564 ( to 3 dec. places )

Explanation:

Using the rule of logarithms

log
`x^(n)` ⇔ n logx

Given

`5^(x)` = 62 ( take the ln of both sides )

ln
`5^(x)` = ln 62, that is

x ln5 = ln 62 ( divide both sides by ln 5 )

x =
`(ln62)/(ln5)` ≈ 2.564