What is 4log_{b}(x)+6log_{b}(z) ?

The solution to 4log_{b}(x)+6log_{b}(z) is log_{b}(x^4z^6)

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simplify 4log_{b}(x)+6log_{b}(z)

simplify

4 lo g_{b} (x) + 6 lo g_{b} (z)

lo g_{b} (x^{4} z^{6})

Solution steps

4 lo g_{b} (x) + 6 lo g_{b} (z)

Apply log rule:

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

4 lo g_{b} (x) = lo g_{b} (x^{4})

= lo g_{b} (x^{4}) + 6 lo g_{b} (z)

Apply log rule:

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

6 lo g_{b} (z) = lo g_{b} (z^{6})

= lo g_{b} (x^{4}) + lo g_{b} (z^{6})

Apply log rule:

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

lo g_{b} (x^{4}) + lo g_{b} (z^{6}) = lo g_{b} (x^{4} z^{6})

= lo g_{b} (x^{4} z^{6})

lo g_{10} (\frac{x ^{2}}{y ^{4}})

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

lo g_{10} (\frac{ab}{c d})

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

lo g_{2} (8 a)

What is 4log_{b}(x)+6log_{b}(z) ?
The solution to 4log_{b}(x)+6log_{b}(z) is log_{b}(x^4z^6)