What is log_{a}(a^2bc^3) ?

The solution to log_{a}(a^2bc^3) is 2+log_{a}(b)+3log_{a}(c)

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simplify log_{a}(a^2bc^3)

simplify

lo g_{a} (a^{2} b c^{3})

2 + lo g_{a} (b) + 3 lo g_{a} (c)

Solution steps

lo g_{a} (a^{2} b c^{3})

Apply log rule:

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

lo g_{a} (a^{2} b c^{3}) = lo g_{a} (a^{2}) + lo g_{a} (b) + lo g_{a} (c^{3})

= lo g_{a} (a^{2}) + lo g_{a} (b) + lo g_{a} (c^{3})

Apply log rule:

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

lo g_{a} (a^{2}) = 2 lo g_{a} (a)

= 2 lo g_{a} (a) + lo g_{a} (b) + lo g_{a} (c^{3})

Apply log rule:

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

lo g_{a} (c^{3}) = 3 lo g_{a} (c)

= 2 lo g_{a} (a) + lo g_{a} (b) + 3 lo g_{a} (c)

2 lo g_{a} (a) = 2

= 2 + lo g_{a} (b) + 3 lo g_{a} (c)

lo g_{10} (2 x - 4) - 0.5 lo g_{10} (x)

ln (\frac{2 ^{0.538 + 1} - 1}{( 0.538 - 1 ) x})

\frac{ln ( x ) - ln ( 4 )}{x - 4}

2 ln (a) - 4 ln (y)

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

What is log_{a}(a^2bc^3) ?
The solution to log_{a}(a^2bc^3) is 2+log_{a}(b)+3log_{a}(c)