What is log_{5}(3x^2)+ln(4x^3) ?

The solution to log_{5}(3x^2)+ln(4x^3) is log_{5}(3)+2log_{5}(x)+2ln(2)+3ln(x)

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simplify log_{5}(3x^2)+ln(4x^3)

simplify

lo g_{5} (3 x^{2}) + ln (4 x^{3})

lo g_{5} (3) + 2 lo g_{5} (x) + 2 ln (2) + 3 ln (x)

Solution steps

lo g_{5} (3 x^{2}) + ln (4 x^{3})

Apply log rule:

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

lo g_{5} (3 x^{2}) = lo g_{5} (3) + lo g_{5} (x^{2}), ln (4 x^{3}) = ln (4) + ln (x^{3})

= lo g_{5} (3) + lo g_{5} (x^{2}) + ln (4) + ln (x^{3})

Apply log rule:

lo g_{a} (x^{b}) = b \cdot lo g_{a} (x)

lo g_{5} (x^{2}) = 2 lo g_{5} (x)

= lo g_{5} (3) + 2 lo g_{5} (x) + ln (4) + ln (x^{3})

Apply log rule:

lo g_{a} (x^{b}) = b \cdot lo g_{a} (x)

ln (x^{3}) = 3 ln (x)

= lo g_{5} (3) + 2 lo g_{5} (x) + ln (4) + 3 ln (x)

ln (4) = 2 ln (2)

= lo g_{5} (3) + 2 lo g_{5} (x) + 2 ln (2) + 3 ln (x)

\frac{1}{11.81 \cdot 1 0 ^{- 4}} ln (\frac{1.3}{0.02})

3 \cdot ln (x) + ln (x^{4}) - ln (x^{3} e^{x})

5 ln (\frac{1 - \frac{2}{2}}{1 + \frac{2}{2}})

\frac{1}{4} ln (15)

ln (\frac{1 - e ^{x}}{1 + e ^{2}})

What is log_{5}(3x^2)+ln(4x^3) ?
The solution to log_{5}(3x^2)+ln(4x^3) is log_{5}(3)+2log_{5}(x)+2ln(2)+3ln(x)