What is log_{10}(3x^3)*ln(10) ?

The solution to log_{10}(3x^3)*ln(10) is ln(3)+3ln(x)

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simplify log_{10}(3x^3)*ln(10)

simplify

lo g_{10} (3 x^{3}) \cdot ln (10)

ln (3) + 3 ln (x)

Solution steps

lo g_{10} (3 x^{3}) ln (10)

Apply log rule:

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

lo g_{10} (3 x^{3}) ln (10) = ln (10) lo g_{10} (3) + ln (10) lo g_{10} (x^{3})

= ln (10) lo g_{10} (3) + ln (10) lo g_{10} (x^{3})

Apply log rule:

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

lo g_{10} (x^{3}) = 3 lo g_{10} (x)

= ln (10) lo g_{10} (3) + ln (10) \cdot 3 lo g_{10} (x)

ln (10) lo g_{10} (3) = ln (3)

ln (10) \cdot 3 lo g_{10} (x) = 3 ln (x)

= ln (3) + 3 ln (x)

ln (\frac{11 π}{2})

ln (x y^{7})

- 0.5 ln (\frac{1}{2}) + \frac{1}{2} ln (\frac{3}{2})

ln (x) - 9 ln (x + 2)

What is log_{10}(3x^3)*ln(10) ?
The solution to log_{10}(3x^3)*ln(10) is ln(3)+3ln(x)