Solve for x (to three decimal places).

Question

10^(2x+1)=0.25

Answer 1

Hi there! I'd love to help you out

When solving for exponents we use logs:

10^(2x+1) = 0.25

log[10^(2x+1)] = log(0.25) Using law of logs, move exponents in front of the log

(2x+1) * log(10) = log(0.25) We know that log(10) is just 1 so it just becomes 1

2x + 1 = log(0.25) Subtract 1 from both sides

2x = log(0.25) - 1 Divide by 2 (or multiply by 1/2)

x = 1/2[log(0.25) - 1] Plug it into your calculator!

x = -0.801

There you have it! I hope this explanation was thorough and answered all of your questions. If you have additional questions please don't hesitate to reach out! Learn on! :)