What is 2log_{b}(z)+3(log_{b}(x)-4log_{b}(w)) ?

The solution to 2log_{b}(z)+3(log_{b}(x)-4log_{b}(w)) is log_{b}((z^2x^3)/(w^{12)})

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simplify 2log_{b}(z)+3(log_{b}(x)-4log_{b}(w))

simplify

2 lo g_{b} (z) + 3 (lo g_{b} (x) - 4 lo g_{b} (w))

lo g_{b} (\frac{z ^{2} x ^{3}}{w ^{12}})

Solution steps

2 lo g_{b} (z) + 3 (lo g_{b} (x) - 4 lo g_{b} (w))

Apply log rule:

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

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

= 2 lo g_{b} (z) + 3 (lo g_{b} (x) - lo g_{b} (w^{4}))

Apply log rule:

lo g_{c} (a) - lo g_{c} (b) = lo g_{c} (\frac{a}{b})

lo g_{b} (x) - lo g_{b} (w^{4}) = lo g_{b} (\frac{x}{w ^{4}})

= 2 lo g_{b} (z) + 3 lo g_{b} (\frac{x}{w ^{4}})

Apply log rule:

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

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

= lo g_{b} (z^{2}) + 3 lo g_{b} (\frac{x}{w ^{4}})

Apply log rule:

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

3 lo g_{b} (\frac{x}{w ^{4}}) = lo g_{b} ((\frac{x}{w ^{4}})^{3})

= lo g_{b} (z^{2}) + lo g_{b} ((\frac{x}{w ^{4}})^{3})

Apply log rule:

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

lo g_{b} (z^{2}) + lo g_{b} ((\frac{x}{w ^{4}})^{3}) = lo g_{b} ((\frac{x}{w ^{4}})^{3} z^{2})

= lo g_{b} ((\frac{x}{w ^{4}})^{3} z^{2})

Simplify

z^{2} (\frac{x}{w ^{4}})^{3} : \frac{z ^{2} x ^{3}}{w ^{12}}

= lo g_{b} (\frac{z ^{2} x ^{3}}{w ^{12}})

- [\frac{3}{5} lo g_{2} (\frac{3}{5}) + \frac{2}{5} lo g_{2} (\frac{2}{5})]

ln (4.98 \cdot 1 0^{15} \cdot e^{0.47 (2000 - 2010)})

lo g_{10} (6) lo g_{10} (2) + lo g_{10} (3)

(\frac{1}{0.143}) ln (\frac{6 \cdot 1 0 ^{9}}{29000})

ln (\frac{547}{273}) \cdot 8

What is 2log_{b}(z)+3(log_{b}(x)-4log_{b}(w)) ?
The solution to 2log_{b}(z)+3(log_{b}(x)-4log_{b}(w)) is log_{b}((z^2x^3)/(w^{12)})