What is expand log_{7}((1/2 m^5)^4) ?

The solution to expand log_{7}((1/2 m^5)^4) is -4log_{7}(2)+20log_{7}(m)

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expand log_{7}((1/2 m^5)^4)

expand

lo g_{7} ((\frac{1}{2} m^{5})^{4})

- 4 lo g_{7} (2) + 20 lo g_{7} (m)

Solution steps

lo g_{7} ((\frac{1}{2} m^{5})^{4})

Apply log rule:

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

lo g_{7} ((\frac{1}{2} m^{5})^{4}) = 4 lo g_{7} (\frac{1}{2} m^{5})

= 4 lo g_{7} (\frac{1}{2} m^{5})

Apply log rule:

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

4 lo g_{7} (\frac{1}{2} m^{5}) = 4 lo g_{7} (\frac{1}{2}) + 4 lo g_{7} (m^{5})

= 4 lo g_{7} (\frac{1}{2}) + 4 lo g_{7} (m^{5})

Apply log rule:

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

lo g_{7} (m^{5}) = 5 lo g_{7} (m)

= 4 lo g_{7} (\frac{1}{2}) + 4 \cdot 5 lo g_{7} (m)

Apply log rule:

lo g_{c} (\frac{a}{b}) = lo g_{c} (a) - lo g_{c} (b)

lo g_{7} (\frac{1}{2}) = lo g_{7} (1) - lo g_{7} (2)

= 4 (lo g_{7} (1) - lo g_{7} (2)) + 4 \cdot 5 lo g_{7} (m)

4 (lo g_{7} (1) - lo g_{7} (2)) = - 4 lo g_{7} (2)

= - 4 lo g_{7} (2) + 4 \cdot 5 lo g_{7} (m)

Multiply the numbers:

4 \cdot 5 = 20

= - 4 lo g_{7} (2) + 20 lo g_{7} (m)

lo g_{10} ((x + 2)^{2}) + lo g_{10} ((x + 1)^{3})

4 ln (7 - 2)

lo g_{2} (\frac{x ^{8} y ^{3}}{8 w ^{2}})

lo g_{10} (\frac{r ^{2} s ^{6}}{t ^{4}})

lo g_{10} (\frac{z ^{3} y ^{2}}{x})

What is expand log_{7}((1/2 m^5)^4) ?
The solution to expand log_{7}((1/2 m^5)^4) is -4log_{7}(2)+20log_{7}(m)