Confusion regarding the Logarithmic function change of base formula
My textbook seems to be making
arridsd9
Answered question
2022-06-21
Confusion regarding the Logarithmic function change of base formula My textbook seems to be making a big leap when trying to prove the change of base formula for logarithms. If someone could help clear this up it would be very appreciated. It starts with:
and uses the power rule to get:
And it equates all this to:
Okay, I get it up to here, but then for me it leaps from that to this:
And it says that divide through by to get the result. What precisely has happened here? Could someone walk me through this step-by-step? Thank you.
Answer & Explanation
massetereqe
Beginner2022-06-22Added 21 answers
I would emphasize these sorts of things:
and
Your third line says
I would take of both sides to get the one i actually remember
That is, to take log with an exponent, pull the exponent in front and apply the log to what remains. To match up (eventually) with your text, let me replace theletter x with a letter t, for
Now, make the purely algebraic substitution
However,
So
Or
Notice how the b's seem to cancel in the fraction on the right hand side. Something to help remember. For example, with we see
Emmy Dillon
Beginner2022-06-23Added 5 answers
according to the rules of logarithms. Also, . I think that this gets you there.