What is 2log_{b}(6)-log_{b}(9) ?

The solution to 2log_{b}(6)-log_{b}(9) is 2log_{b}(2)

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simplify 2log_{b}(6)-log_{b}(9)

simplify

2 lo g_{b} (6) - lo g_{b} (9)

2 lo g_{b} (2)

Solution steps

2 lo g_{b} (6) - lo g_{b} (9)

Apply log rule:

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

2 lo g_{b} (6) = lo g_{b} (6^{2})

= lo g_{b} (6^{2}) - lo g_{b} (9)

Apply log rule:

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

lo g_{b} (6^{2}) - lo g_{b} (9) = lo g_{b} (\frac{6 ^{2}}{9})

= lo g_{b} (\frac{6 ^{2}}{9})

\frac{6 ^{2}}{9} = 4

= lo g_{b} (4)

Factor the number:

4 = 2^{2}

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

Apply log rule:

lo g_{a} (x^{b}) = b \cdot lo g_{a} (x), x > 0

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

= 2 lo g_{b} (2)

\frac{1}{2} lo g_{10} (x) - 3 lo g_{10} (y) - lo g_{10} (z)

ln (\frac{81}{125})

ln (x) - 2 ln (y)

lo g_{10} (\frac{a ^{6}}{b ^{5} c})

lo g_{10} (5) + lo g_{10} (x)

What is 2log_{b}(6)-log_{b}(9) ?
The solution to 2log_{b}(6)-log_{b}(9) is 2log_{b}(2)