What is 2log_{10}(a)+4log_{10}(b^2)-log_{10}(a)b ?

The solution to 2log_{10}(a)+4log_{10}(b^2)-log_{10}(a)b is log_{10}(a^{2-b}b^8)

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simplify 2log_{10}(a)+4log_{10}(b^2)-log_{10}(a)b

simplify

2 lo g_{10} (a) + 4 lo g_{10} (b^{2}) - lo g_{10} (a) b

lo g_{10} (a^{2 - b} b^{8})

Solution steps

2 lo g_{10} (a) + 4 lo g_{10} (b^{2}) - lo g_{10} (a) b

Simplify

4 lo g_{10} (b^{2}) : 8 lo g_{10} (b)

= 2 lo g_{10} (a) + 8 lo g_{10} (b) - lo g_{10} (a) b

2 lo g_{10} (a) = lo g_{10} (a^{2})

8 lo g_{10} (b) = lo g_{10} (b^{8})

- lo g_{10} (a) b = - lo g_{10} (a^{b})

= lo g_{10} (a^{2}) + lo g_{10} (b^{8}) - lo g_{10} (a^{b})

Apply log rule:

lo g_{a} (x) + lo g_{a} (y) = lo g_{a} (x y)

lo g_{10} (a^{2}) + lo g_{10} (b^{8}) = lo g_{10} (a^{2} b^{8})

= lo g_{10} (a^{2} b^{8}) - lo g_{10} (a^{b})

Apply log rule:

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

lo g_{10} (a^{2} b^{8}) - lo g_{10} (a^{b}) = lo g_{10} (\frac{a ^{2} b ^{8}}{a ^{b}})

= lo g_{10} (\frac{a ^{2} b ^{8}}{a ^{b}})

Simplify

\frac{a ^{2} b ^{8}}{a ^{b}} : a^{2 - b} b^{8}

= lo g_{10} (a^{2 - b} b^{8})

ln (2.5 \cdot 1 0^{- 3}) + (\frac{130000}{8.314 \cdot 473})

ln (\frac{1}{2} x + 4 + x^{2})

lo g_{4} (x + 3) + lo g_{4} (x - 3)

lo g_{a} (\frac{x ^{\frac{1}{2}} y ^{5}}{x ^{3}})

lo g_{10} (\frac{p ^{6}}{q ^{1}})

What is 2log_{10}(a)+4log_{10}(b^2)-log_{10}(a)b ?
The solution to 2log_{10}(a)+4log_{10}(b^2)-log_{10}(a)b is log_{10}(a^{2-b}b^8)