What is 5(log_{5}(3)+log_{5}(b))-log_{5}(4) ?

The solution to 5(log_{5}(3)+log_{5}(b))-log_{5}(4) is log_{5}((243b^5)/4)

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simplify 5(log_{5}(3)+log_{5}(b))-log_{5}(4)

simplify

5 (lo g_{5} (3) + lo g_{5} (b)) - lo g_{5} (4)

lo g_{5} (\frac{243 b ^{5}}{4})

Solution steps

5 (lo g_{5} (3) + lo g_{5} (b)) - lo g_{5} (4)

lo g_{5} (3) + lo g_{5} (b) = lo g_{5} (3 b)

lo g_{5} (4) = 2 lo g_{5} (2)

= 5 lo g_{5} (3 b) - 2 lo g_{5} (2)

5 lo g_{5} (3 b) = lo g_{5} ((3 b)^{5})

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

= lo g_{5} ((3 b)^{5}) - lo g_{5} (2^{2})

Apply log rule:

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

lo g_{5} ((3 b)^{5}) - lo g_{5} (2^{2}) = lo g_{5} (\frac{( 3 b ) ^{5}}{2 ^{2}})

= lo g_{5} (\frac{( 3 b ) ^{5}}{2 ^{2}})

Simplify

\frac{( 3 b ) ^{5}}{2 ^{2}} : \frac{243 b ^{5}}{4}

= lo g_{5} (\frac{243 b ^{5}}{4})

- lo g_{10} (4 \times 1 0^{- 4})

ln (9 e) + ln (e^{9}) + ln (4) e^{4}

6 [4 ln (x) - ln (x + 5) - ln (x - 5)]

lo g_{3} (\frac{x - 1 ^{4}}{x + 1 ^{9}})

What is 5(log_{5}(3)+log_{5}(b))-log_{5}(4) ?
The solution to 5(log_{5}(3)+log_{5}(b))-log_{5}(4) is log_{5}((243b^5)/4)