Logarithm problems with different bases 1.log_ab*\log_ba=? 2.log_ab+log_ba=sqrt(29)

Kubaczynjo

Kubaczynjo

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2022-08-30

Logarithm problems with different bases
1. log a b × log b a =?
2. log a b + log b a = 29
What is log a b log b a =?
3.
What is b in the following:
log b 3 + log b 11 + log b 61 = 1
and
4.
1 l o g 2 x + 1 l o g 25 x 3 log 8 x = 1 log b x
What is b?
Can anyone help me solve these?

Answer & Explanation

betoosolis7i

betoosolis7i

Beginner2022-08-31Added 12 answers

The way to start all of these and turn them into simple algebra is that log a b = log x b log x a Using that formula, all of these become basic algebra. Give it a try and comment what you get.
Nezveda6q

Nezveda6q

Beginner2022-09-01Added 7 answers

2 . let x = log a b = 1 log b a
log a b + 1 log a b = 29
Then log a b and log a b are solutions of the following equation
x + 1 x = 29
x 1 = 29 5 2 = log b a
x 2 = 29 + 5 2 = log a b
(We assume that a < b ) Thus log a b log b a = 29 + 5 2 29 5 2 = 5
4.
1 l o g 2 x + 1 l o g 25 x 3 log 8 x = 1 log b x
Using formula log a b = 1 log b a we have
log x 2 + log x 25 3 l o g x 8 = log x b
Use formulas
log x a + log x c = log x a c
and
n log x a = log x a n

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