What is 3log_{b}(4x)-(log_{b}(5y)+log_{b}(6z)) ?

The solution to 3log_{b}(4x)-(log_{b}(5y)+log_{b}(6z)) is log_{b}((32x^3)/(15yz))

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simplify 3log_{b}(4x)-(log_{b}(5y)+log_{b}(6z))

simplify

3 lo g_{b} (4 x) - (lo g_{b} (5 y) + lo g_{b} (6 z))

lo g_{b} (\frac{32 x ^{3}}{15 yz})

Solution steps

3 lo g_{b} (4 x) - (lo g_{b} (5 y) + lo g_{b} (6 z))

Simplify

lo g_{b} (5 y) + lo g_{b} (6 z) : lo g_{b} (30 yz)

= 3 lo g_{b} (4 x) - lo g_{b} (30 yz)

Apply log rule:

b \cdot lo g_{a} (x) = lo g_{a} (x^{b})

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

= lo g_{b} ((4 x)^{3}) - lo g_{b} (30 yz)

Apply log rule:

lo g_{a} (x) - lo g_{a} (y) = lo g_{a} (\frac{x}{y})

lo g_{b} ((4 x)^{3}) - lo g_{b} (30 yz) = lo g_{b} (\frac{( 4 x ) ^{3}}{30 yz})

= lo g_{b} (\frac{( 4 x ) ^{3}}{30 yz})

Simplify

\frac{( 4 x ) ^{3}}{30 yz} : \frac{32 x ^{3}}{15 yz}

= lo g_{b} (\frac{32 x ^{3}}{15 yz})

lo g_{10} (\frac{15}{x y})

ln (e^{x}) - ln (1 + e^{x})

2 + lo g_{10} (x) + lo g_{10} (y)

lo g_{10} (\frac{z}{x ^{7}})

2 lo g_{10} (p) + 5 lo g_{10} (q) - lo g_{10} (r)

What is 3log_{b}(4x)-(log_{b}(5y)+log_{b}(6z)) ?
The solution to 3log_{b}(4x)-(log_{b}(5y)+log_{b}(6z)) is log_{b}((32x^3)/(15yz))