What is 4log_{b}(y)+3log_{b}(x) ?

The solution to 4log_{b}(y)+3log_{b}(x) is log_{b}(y^4x^3)

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simplify 4log_{b}(y)+3log_{b}(x)

simplify

4 lo g_{b} (y) + 3 lo g_{b} (x)

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

Solution steps

4 lo g_{b} (y) + 3 lo g_{b} (x)

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} (y^{4}) + 3 lo g_{b} (x)

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} (y^{4}) + lo g_{b} (x^{3})

Apply log rule:

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

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

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

2 ln (x) - 4 ln (\frac{1}{y}) - 3 ln (x y)

- 3 ln (2) + ln (3) + 3

ln (\frac{c}{ab})

10 \cdot lo g_{10} (0.1 \cdot (\frac{0.125}{4 \cdot π \cdot 8})^{2})

ln (\frac{1}{2}) \cdot ln (\frac{1}{2})

What is 4log_{b}(y)+3log_{b}(x) ?
The solution to 4log_{b}(y)+3log_{b}(x) is log_{b}(y^4x^3)