Question

Need a step-by-step please. Logarithms.

Answer 1

How do I do this?

Answer 2

b^0.792 = 3
can you calculate log b from here ?

Answer 3

say, for base 10

Answer 4

log b 3 = 0.792?

Answer 5

Not sure how, no.

Answer 6

log b = (log 3)/0.792
base of the log is 10

Answer 7

How did you get to (log3)/0.792?

Answer 8

log (p^q) = q* log p

Answer 9

do you know log(ab) = loga + logb ?

Answer 10

Yea. But I am still confused, can you start from the beginning?

Answer 11

Where did p come from?

Answer 12

Let me try to explain this identity : log (p^q) = q* log p
think it as log (p. p^(q-1) ) = log p + log (p^(q-1) ) = log p + log(p . p^(q-2) ) = log p + log p + log(p^(q-2) ) ...and so on.
therefore , log(p^q) = q * log p
is the identity clear ?

Answer 13

You are bringing the superscript out in front. So log(p^q-2) is like (q-2)logp?

Answer 14

yes.

Answer 15

Alright. So far so good.

Answer 16

Now, in case of b^0.792 = 3
when you take log on both sides,
you get 0.792 log b = log 3

Answer 17

Then dividing you get (log3)/0.792 = logb?

Answer 18

yes.

Answer 19

Now you must remember the value of log 3 ?

Answer 20

0.477 approx

Answer 21

But these aren't exact answers right? Isn't there a way to determine what b is in exact terms?

Answer 22

exactly b will be 10^(log3/0.792)

Answer 23

but you need to approximate it /

Answer 24

I get it! I can figure it out from here. Thank you so much @shubhamsrg

Answer 25

Okay, glad to help. :)