How do you solve 8^x=1000?

2 Answers
Nov 28, 2016

x~~3.322

Explanation:

Convert the exponential form to a logarithmic form a^x=b-> x=log_ab

8^x=1000

x=log_8 1000

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

log_a b = (log_c b)/(log_c a)" " (c is usually 10)

x = log_10 1000//log_10 8

x~~3.322

Nov 29, 2016

x≈3.322

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.

rArrxln8=ln1000

divide both sides by ln8

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

rArrx≈3.322" to 3 decimal places"