Find the solution log(6x+10) = log(x)/log(1/2)

Zoe Oneal 2021-01-31 Answered
Find the solution log(6x+10)=log(x)log(12)
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Expert Answer

AGRFTr
Answered 2021-02-01 Author has 95 answers

The solution is x=0.464343 approx. using the Intermediate Value Theorem.
METHOD
The quantity on the right can only be positive when 0 The domain can be split into 0.1 intervals, and by substituting x=0.1 to 0.9 in the expression log(6x+10)log(x)log(12) where log is assumed to be base 10, it can be seen that the expression changes sign between 0.4 and 0.5.
This interval can be split into hundredths: 0.40, 0.41, ,0.49, 0.50 and re-evaluated. By continuing this process an approximate value of x can be found.
If the logs are natural logs x=0.188211 approx.
Note that 1log10(12)=log[base12](10), so the question can be expressed:
log(6x+10)=log(x)log[base12] (10) and log[base12](x)=log2(x).

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