What is 7log_{b}(x)+8log_{b}(z) ?

The solution to 7log_{b}(x)+8log_{b}(z) is log_{b}(x^7z^8)

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simplify 7log_{b}(x)+8log_{b}(z)

simplify

7 lo g_{b} (x) + 8 lo g_{b} (z)

lo g_{b} (x^{7} z^{8})

Solution steps

7 lo g_{b} (x) + 8 lo g_{b} (z)

Apply log rule:

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

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

= lo g_{b} (x^{7}) + 8 lo g_{b} (z)

Apply log rule:

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

8 lo g_{b} (z) = lo g_{b} (z^{8})

= lo g_{b} (x^{7}) + lo g_{b} (z^{8})

Apply log rule:

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

lo g_{b} (x^{7}) + lo g_{b} (z^{8}) = lo g_{b} (x^{7} z^{8})

= lo g_{b} (x^{7} z^{8})

lo g_{2} (3 c)

\frac{1}{31} (ln (x) + ln (y))

ln (8) + \frac{1}{2} ln (x + 1) - 3 ln (1 + x)

\frac{1}{2} ln (x) + 8 ln (y) - 9 ln (z)

ln (\frac{9}{49})

What is 7log_{b}(x)+8log_{b}(z) ?
The solution to 7log_{b}(x)+8log_{b}(z) is log_{b}(x^7z^8)