What is 3log_{b}(x)+log_{b}(2y)-1 ?

The solution to 3log_{b}(x)+log_{b}(2y)-1 is log_{b}(x^3*2y)-1

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simplify 3log_{b}(x)+log_{b}(2y)-1

simplify

3 lo g_{b} (x) + lo g_{b} (2 y) - 1

lo g_{b} (x^{3} \cdot 2 y) - 1

Solution steps

3 lo g_{b} (x) + lo g_{b} (2 y) - 1

Apply log rule:

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

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

= lo g_{b} (x^{3}) + lo g_{b} (2 y) - 1

Apply log rule:

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

lo g_{b} (x^{3}) + lo g_{b} (2 y) = lo g_{b} (2 x^{3} y)

= lo g_{b} (x^{3} \cdot 2 y) - 1

ln (e^{3} x)

ln (5) - ln (x)

ln (1.5) - ln (0.6)

ln (\frac{16}{81})

lo g_{10} (4) + 3 lo g_{10} (0.235)

What is 3log_{b}(x)+log_{b}(2y)-1 ?
The solution to 3log_{b}(x)+log_{b}(2y)-1 is log_{b}(x^3*2y)-1