What is 5log_{7}(a)+10log_{7}(b) ?

The solution to 5log_{7}(a)+10log_{7}(b) is log_{7}(a^5b^{10})

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simplify 5log_{7}(a)+10log_{7}(b)

simplify

5 lo g_{7} (a) + 10 lo g_{7} (b)

lo g_{7} (a^{5} b^{10})

Solution steps

5 lo g_{7} (a) + 10 lo g_{7} (b)

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}) + 10 lo g_{7} (b)

Apply log rule:

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

10 lo g_{7} (b) = lo g_{7} (b^{10})

= lo g_{7} (a^{5}) + lo g_{7} (b^{10})

Apply log rule:

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

lo g_{7} (a^{5}) + lo g_{7} (b^{10}) = lo g_{7} (a^{5} b^{10})

= lo g_{7} (a^{5} b^{10})

ln (3 x) + ln (2 x^{2})

- lo g_{2} (\frac{1}{48})

\frac{ln ( 2.1 ) - ln ( 2 )}{2.1 - 2}

lo g_{10} (x z^{8})

ln (9) - ln (6)

What is 5log_{7}(a)+10log_{7}(b) ?
The solution to 5log_{7}(a)+10log_{7}(b) is log_{7}(a^5b^{10})