What is 6log_{2}(x-5)-log_{2}(y)+log_{2}(x) ?

The solution to 6log_{2}(x-5)-log_{2}(y)+log_{2}(x) is log_{2}((x(x-5)^6)/y)

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simplify 6log_{2}(x-5)-log_{2}(y)+log_{2}(x)

simplify

6 lo g_{2} (x - 5) - lo g_{2} (y) + lo g_{2} (x)

lo g_{2} (\frac{x ( x - 5 ) ^{6}}{y})

Solution steps

6 lo g_{2} (x - 5) - lo g_{2} (y) + lo g_{2} (x)

Apply log rule:

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

6 lo g_{2} (x - 5) = lo g_{2} ((x - 5)^{6})

= lo g_{2} ((x - 5)^{6}) - lo g_{2} (y) + lo g_{2} (x)

Apply log rule:

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

lo g_{2} ((x - 5)^{6}) - lo g_{2} (y) = lo g_{2} (\frac{( x - 5 ) ^{6}}{y})

= lo g_{2} (\frac{( x - 5 ) ^{6}}{y}) + lo g_{2} (x)

Apply log rule:

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

lo g_{2} (\frac{( x - 5 ) ^{6}}{y}) + lo g_{2} (x) = lo g_{2} (\frac{( x - 5 ) ^{6}}{y} x)

= lo g_{2} (\frac{( x - 5 ) ^{6}}{y} x)

Multiply fractions:

a \cdot \frac{b}{c} = \frac{a \cdot b}{c}

= lo g_{2} (\frac{x ( x - 5 ) ^{6}}{y})

ln (6) - 2 + 2 ln (x)

ln (u) + ln (k)

\frac{1}{3} ln (2) + \frac{1}{3} ln (10)

\frac{ln ( 1.4 ) - 5 ln ( 1.05 )}{2 ln ( 1.05 )}

What is 6log_{2}(x-5)-log_{2}(y)+log_{2}(x) ?
The solution to 6log_{2}(x-5)-log_{2}(y)+log_{2}(x) is log_{2}((x(x-5)^6)/y)