Simplifying Logarithmic Expression Compute: \frac{1-\log_a^{3}b }{(\log_a b+\log_b a+1)\log_a\frac{a}{b}} I tried to expand it

zergingk8l

zergingk8l

Answered question

2022-04-25

Simplifying Logarithmic Expression
Compute:
1loga3b(logab+logba+1)logaab
I tried to expand it :
1loga3b(logab+logba+1)logaab
=(1logab)(loga2b+logab+1)(logab+logba+1)(1logab)
=(loga2b+logab+1)(logab+logba+1)
But I got nothing.

Answer & Explanation

Cristal Roth

Cristal Roth

Beginner2022-04-26Added 13 answers

I think this should help you.
logba=logaalogab=1logab
Can you finish it from here?
narratz5dz

narratz5dz

Beginner2022-04-27Added 13 answers

You also could use
logaab=logaalogab=1logab
logba=1logab
You can express everything in terms of logab. If you substitute this for readability by, say, x the rest is basic. And to test your result it should be just logab.

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