What is expand log_{4}(a^7b^3) ?

The solution to expand log_{4}(a^7b^3) is 7log_{4}(a)+3log_{4}(b)

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expand log_{4}(a^7b^3)

expand

lo g_{4} (a^{7} b^{3})

7 lo g_{4} (a) + 3 lo g_{4} (b)

Solution steps

lo g_{4} (a^{7} b^{3})

Apply log rule:

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

lo g_{4} (a^{7} b^{3}) = lo g_{4} (a^{7}) + lo g_{4} (b^{3})

= lo g_{4} (a^{7}) + lo g_{4} (b^{3})

Apply log rule:

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

lo g_{4} (a^{7}) = 7 lo g_{4} (a)

= 7 lo g_{4} (a) + lo g_{4} (b^{3})

Apply log rule:

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

lo g_{4} (b^{3}) = 3 lo g_{4} (b)

= 7 lo g_{4} (a) + 3 lo g_{4} (b)

8.314 \cdot ln (\frac{1}{10})

\frac{1}{1.21 \cdot 1 0 ^{- 4}} ln (\frac{12.5}{100})

ln (9.4 \cdot 1 0^{- 5})

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

ln (x y) + 7 ln (\frac{y}{z}) - 5 ln (x yz)

What is expand log_{4}(a^7b^3) ?
The solution to expand log_{4}(a^7b^3) is 7log_{4}(a)+3log_{4}(b)