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

The solution to 2(log_{b}(x)-4log_{b}(y))+2log_{b}(z) is log_{b}((x^2z^2)/(y^8))

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

simplify

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

lo g_{b} (\frac{x ^{2} z ^{2}}{y ^{8}})

Solution steps

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

Apply log rule:

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

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

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

Apply log rule:

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

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

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

Apply log rule:

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

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

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

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} ((\frac{x}{y ^{4}})^{2}) + lo g_{b} (z^{2})

Apply log rule:

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

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

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

Simplify

(\frac{x}{y ^{4}})^{2} z^{2} : \frac{x ^{2} z ^{2}}{y ^{8}}

= lo g_{b} (\frac{x ^{2} z ^{2}}{y ^{8}})

ln (\frac{( 3 x - 5 ) ^{0.5}}{7})

\frac{97}{100} \cdot ln (3 \cdot 1 0^{6}) + \frac{3}{100} \cdot ln (3000)

e^{\frac{l n ( 3 ) + l n ( 5 )}{2}}

7 lo g_{m} (z) - \frac{1}{2} lo g_{m} (w) + 5 lo g_{m} (x)

0 ln (\frac{\frac{20000}{17} - 1}{1199})

What is 2(log_{b}(x)-4log_{b}(y))+2log_{b}(z) ?
The solution to 2(log_{b}(x)-4log_{b}(y))+2log_{b}(z) is log_{b}((x^2z^2)/(y^8))