Prove the power property of logarithms : \log_bx^p=p\log_bx

Tazmin Horton

Tazmin Horton

Answered question

2021-11-05

Prove the power property of logarithms :
logbxp=plogbx

Answer & Explanation

Jayden-James Duffy

Jayden-James Duffy

Skilled2021-11-06Added 91 answers

Let q=logbx
Equation (1) can be written in exponential form as x=bq
Then,
(xp)=(bq)p,     {  since, raise power p}
(xp)=bqp,     {by using the property of exponent}
logb(x)p=qp,  write in logarithmic form
logb(x)p=plogbx,{  since,  q=logbx}
Thus,  logb(x)p=plogbx
Hence, proved

Do you have a similar question?

Recalculate according to your conditions!

Ask your question.
Get an expert answer.

Let our experts help you. Answer in as fast as 15 minutes.

Didn't find what you were looking for?