What is 5log_{7}(a)-2log^b_{7}(x) ?

The solution to 5log_{7}(a)-2log^b_{7}(x) is log_{7}((a^5)/(x^2))

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simplify 5log_{7}(a)-2log^b_{7}(x)

simplify

5 lo g_{7} (a) - 2 lo g_{7}^{b} (x)

lo g_{7} (\frac{a ^{5}}{x ^{2}})

Solution steps

5 lo g_{7} (a) - 2 lo g_{7}^{b} (x)

Apply log rule:

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

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

= lo g_{7} (a^{5}) - 2 lo g_{7}^{b} (x)

Apply log rule:

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

2 lo g_{7}^{b} (x) = lo g_{7}^{b} (x^{2})

= lo g_{7} (a^{5}) - lo g_{7}^{b} (x^{2})

Apply log rule:

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

lo g_{7} (a^{5}) - lo g_{7}^{b} (x^{2}) = lo g_{7} (\frac{a ^{5}}{x ^{2}})

= lo g_{7} (\frac{a ^{5}}{x ^{2}})

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What is 5log_{7}(a)-2log^b_{7}(x) ?
The solution to 5log_{7}(a)-2log^b_{7}(x) is log_{7}((a^5)/(x^2))