What is log_{10}(5a)+log_{10}(4b) ?

The solution to log_{10}(5a)+log_{10}(4b) is 1+log_{10}(2ab)

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simplify log_{10}(5a)+log_{10}(4b)

simplify

lo g_{10} (5 a) + lo g_{10} (4 b)

1 + lo g_{10} (2 ab)

Solution steps

lo g_{10} (5 a) + lo g_{10} (4 b)

Apply log rule:

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

lo g_{10} (5 a) + lo g_{10} (4 b) = lo g_{10} (5 a \cdot 4 b)

= lo g_{10} (5 a \cdot 4 b)

Simplify

5 a \cdot 4 b : 20 ab

= lo g_{10} (20 ab)

Apply log rule:

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

lo g_{10} (20 ab) = lo g_{10} (20) + lo g_{10} (a) + lo g_{10} (b)

= lo g_{10} (20) + lo g_{10} (a) + lo g_{10} (b)

lo g_{10} (20) = 1 + lo g_{10} (2)

= 1 + lo g_{10} (2) + lo g_{10} (a) + lo g_{10} (b)

Simplify

lo g_{10} (2) + lo g_{10} (a) + lo g_{10} (b) : lo g_{10} (2 ab)

= 1 + lo g_{10} (2 ab)

lo g_{4} (\frac{1}{x})

6 ln (x) + 3 ln (y) - 2 ln (z)

lo g_{7} (\frac{49 b ^{7} y ^{2} - 2}{y ( x + 2 ) ^{2}})

lo g_{10} (\frac{1}{a ^{2}})

What is log_{10}(5a)+log_{10}(4b) ?
The solution to log_{10}(5a)+log_{10}(4b) is 1+log_{10}(2ab)