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

The solution to log_{b}(6x)+5log_{b}(x)-4log_{b}(y) is log_{b}((6x^6)/(y^4))

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

simplify

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

lo g_{b} (\frac{6 x ^{6}}{y ^{4}})

Solution steps

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

Apply log rule:

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

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

= lo g_{b} (6 x) + lo g_{b} (x^{5}) - 4 lo g_{b} (y)

Apply log rule:

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

lo g_{b} (6 x) + lo g_{b} (x^{5}) = lo g_{b} (6 x^{5} x)

= lo g_{b} (6 x^{5} x) - 4 lo g_{b} (y)

Simplify

6 x x^{5} : 6 x^{6}

= lo g_{b} (6 x^{6}) - 4 lo g_{b} (y)

Apply log rule:

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

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

= lo g_{b} (6 x^{6}) - lo g_{b} (y^{4})

Apply log rule:

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

lo g_{b} (6 x^{6}) - lo g_{b} (y^{4}) = lo g_{b} (\frac{6 x ^{6}}{y ^{4}})

= lo g_{b} (\frac{6 x ^{6}}{y ^{4}})

ln (\frac{( λ ^{(x_{1})} e ^{(- λ)} )}{( x _{1} ! )})

0.026 ln (5 \cdot 1 0^{8})

lo g_{a} (a^{2} b c^{3})

lo g_{10} (2 x - 4) - 0.5 lo g_{10} (x)

ln (\frac{2 ^{0.538 + 1} - 1}{( 0.538 - 1 ) x})

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