What is expand log_{2}((a^5b^2)^3) ?

The solution to expand log_{2}((a^5b^2)^3) is 15log_{2}(a)+6log_{2}(b)

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expand log_{2}((a^5b^2)^3)

expand

lo g_{2} ((a^{5} b^{2})^{3})

15 lo g_{2} (a) + 6 lo g_{2} (b)

Solution steps

lo g_{2} ((a^{5} b^{2})^{3})

Apply log rule:

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

lo g_{2} ((a^{5} b^{2})^{3}) = 3 lo g_{2} (a^{5} b^{2})

= 3 lo g_{2} (a^{5} b^{2})

Apply log rule:

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

3 lo g_{2} (a^{5} b^{2}) = 3 lo g_{2} (a^{5}) + 3 lo g_{2} (b^{2})

= 3 lo g_{2} (a^{5}) + 3 lo g_{2} (b^{2})

Apply log rule:

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

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

= 3 \cdot 5 lo g_{2} (a) + 3 lo g_{2} (b^{2})

Apply log rule:

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

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

= 3 \cdot 5 lo g_{2} (a) + 3 \cdot 2 lo g_{2} (b)

Multiply the numbers:

3 \cdot 5 = 15

= 15 lo g_{2} (a) + 3 \cdot 2 lo g_{2} (b)

Multiply the numbers:

3 \cdot 2 = 6

= 15 lo g_{2} (a) + 6 lo g_{2} (b)

1000 e^{\frac{4 l n ( 2 )}{3}}

ln (\frac{( t + 5 ) ^{3}}{t ^{4} ( 5 - 1 ) ^{2}})

ln (x^{5}) - ln (x)

- 4 ln (x) + ln (5 y) - ln (4 z)

\frac{1}{3} lo g_{10} (a) - \frac{1}{2} (lo g_{10} (b) - lo g_{10} (c))

What is expand log_{2}((a^5b^2)^3) ?
The solution to expand log_{2}((a^5b^2)^3) is 15log_{2}(a)+6log_{2}(b)