What is 2log_{b}(x)+5log_{b}(z) ?

The solution to 2log_{b}(x)+5log_{b}(z) is log_{b}(x^2z^5)

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simplify 2log_{b}(x)+5log_{b}(z)

simplify

2 lo g_{b} (x) + 5 lo g_{b} (z)

lo g_{b} (x^{2} z^{5})

Solution steps

2 lo g_{b} (x) + 5 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}) + 5 lo g_{b} (z)

Apply log rule:

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

5 lo g_{b} (z) = lo g_{b} (z^{5})

= lo g_{b} (x^{2}) + lo g_{b} (z^{5})

Apply log rule:

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

lo g_{b} (x^{2}) + lo g_{b} (z^{5}) = lo g_{b} (x^{2} z^{5})

= lo g_{b} (x^{2} z^{5})

lo g_{10} (10 x^{3} y)

ln (\frac{1}{2} x + 2 + x^{2} + 4 x + 8) + C

- 0.03 \cdot ln (\frac{( 1 - 4.1 )}{82})

lo g_{10} (4 θ^{4} (1 - θ)^{4} (1 - 2 θ)^{2})

ln (x (x + 6))

What is 2log_{b}(x)+5log_{b}(z) ?
The solution to 2log_{b}(x)+5log_{b}(z) is log_{b}(x^2z^5)