What is log_{10}(2x-3)+1/3 ln(27x) ?

The solution to log_{10}(2x-3)+1/3 ln(27x) is log_{10}(2x-3)+ln(3)+1/3 ln(x)

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simplify log_{10}(2x-3)+1/3 ln(27x)

simplify

lo g_{10} (2 x - 3) + \frac{1}{3} ln (27 x)

lo g_{10} (2 x - 3) + ln (3) + \frac{1}{3} ln (x)

Solution steps

lo g_{10} (2 x - 3) + \frac{1}{3} ln (27 x)

Apply log rule:

lo g_{c} (ab) = lo g_{c} (a) + lo g_{c} (b)

\frac{1}{3} ln (27 x) = \frac{1}{3} ln (27) + \frac{1}{3} ln (x)

= lo g_{10} (2 x - 3) + \frac{1}{3} ln (27) + \frac{1}{3} ln (x)

\frac{1}{3} ln (27) = ln (3)

= lo g_{10} (2 x - 3) + ln (3) + \frac{1}{3} ln (x)

\frac{ln ^{2} ( 6 x ) - ln ^{2} ( 3 x ) + 2 ln ( 2 )}{2}

lo g_{10} (\frac{x ^{2}}{4 y ^{3}})

lo g_{5} (\frac{7 z}{6})

\frac{1}{2} lo g_{10} (5)

What is log_{10}(2x-3)+1/3 ln(27x) ?
The solution to log_{10}(2x-3)+1/3 ln(27x) is log_{10}(2x-3)+ln(3)+1/3 ln(x)