What is 2log_{b}(x)+7log_{b}(z) ?

The solution to 2log_{b}(x)+7log_{b}(z) is log_{b}(x^2z^7)

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simplify 2log_{b}(x)+7log_{b}(z)

simplify

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

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

Solution steps

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

Apply log rule:

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

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

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

Apply log rule:

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

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

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

Apply log rule:

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

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

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

lo g_{4} (\frac{ab}{c d})

ln (x - 2) - ln (2 x - 3)

lo g_{10} (5 x) - 7 (10 x - 2)

ln (\frac{6 x}{x ^{2} - 4})

lo g_{5} (4) + lo g_{5} (10)

What is 2log_{b}(x)+7log_{b}(z) ?
The solution to 2log_{b}(x)+7log_{b}(z) is log_{b}(x^2z^7)