Simplify a logarithm function 2\log\sqrt[4]{10}-\ln e^{-7}+\log_9\sqrt 3 I want to simplify this

Terrence Moore

Terrence Moore

Answered question

2022-05-01

Simplify a logarithm function
2log104-lne-7+log93
I want to simplify this function. I believe that 2log104 can become log10 but now I'm stuck.
Is it possible that lne7 can be just 7?

Answer & Explanation

eldgamliru9x

eldgamliru9x

Beginner2022-05-02Added 16 answers

log104=14log10
lne7=7lne=71
log93=12log93=12log99=1212=14
Probably "log10" is intended to mean log1010, so that is equal to 1.
I disapprove of using "log " with no base to mean log10 when there's no special context saying that's the right base to use.

Cristal Roth

Cristal Roth

Beginner2022-05-03Added 13 answers

2log104-lne-7+log93=24log10-(-7)+12log93=12+7+14
Properties used:
logaan=n,      logaxn=nlogax
and, of course, the very definition of logarithm and the assumed fact that you surely meant log=log10

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