# How do you solve #8^x=1000#?

##### 2 Answers

#### Explanation:

Convert the exponential form to a logarithmic form

You can use the 'change of base law' to calculate it.

Nov 29, 2016

#### Explanation:

Use the

#color(blue)"law of logarithms"#

#color(red)(bar(ul(|color(white)(2/2)color(black)(logx^n=nlogx)color(white)(2/2)|)))#

Applies to logarithms to any base.Take the ln ( natural log) of both sides.

#rArrln8^x=ln1000# Using the above law.

divide both sides by ln8

#(x cancel(ln8))/cancel(ln8)=ln1000/ln8#

#rArrx≈3.322" to 3 decimal places"#