What is 2log_{b}(x)+6log_{b}(z) ?

The solution to 2log_{b}(x)+6log_{b}(z) is log_{b}(x^2z^6)

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simplify 2log_{b}(x)+6log_{b}(z)

simplify

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

lo g_{b} (x^{2} z^{6})

Solution steps

2 lo g_{b} (x) + 6 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}) + 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^{2}) + lo g_{b} (z^{6})

Apply log rule:

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

lo g_{b} (x^{2}) + lo g_{b} (z^{6}) = lo g_{b} (x^{2} z^{6})

= lo g_{b} (x^{2} z^{6})

lo g_{2} (\frac{( 2 x ^{6} )}{y})

lo g_{a} (x^{2} - 4) - lo g_{a} (x - 2)

lo g_{4} (\frac{5 x}{y})

lo g_{10} (1000000 y)

lo g_{3} (11 x (3 x + 4))

What is 2log_{b}(x)+6log_{b}(z) ?
The solution to 2log_{b}(x)+6log_{b}(z) is log_{b}(x^2z^6)