How do you solve 3log_10 x+1 = 133log10x+1=13?

1 Answer
Cesareo R.
May 25, 2016

x=10^4x=104

Explanation:

3log_{10}x+1=log_{10}x^3+log_{10}10=13=log_{10}10^{13}3log10x+1=log10x3+log1010=13=log101013
or equivalently
log_{10}(10*x^3) = log_{10}10^{13}log10(10⋅x3)=log101013
or equivalently
10*x^3=10^{13}10⋅x3=1013
concluding that
x^3 = 10^{12}->x=10^4x3=1012→x=104

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