What is log_{x}(sqrt(5))+log_{x}(5x)-2.25 ?

The solution to log_{x}(sqrt(5))+log_{x}(5x)-2.25 is log_{x}(5sqrt(5))-1.25

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simplify log_{x}(sqrt(5))+log_{x}(5x)-2.25

simplify

lo g_{x} (5) + lo g_{x} (5 x) - 2.25

lo g_{x} (55) - 1.25

Solution steps

lo g_{x} (5) + lo g_{x} (5 x) - 2.25

Simplify

lo g_{x} (5 x) : lo g_{x} (5) + 1

= lo g_{x} (5) + (lo g_{x} (5) + 1) - 2.25

Apply rule:

a + (b + c) = a + b + c

lo g_{x} (5) + (lo g_{x} (5) + 1) = lo g_{x} (5) + lo g_{x} (5) + 1

= lo g_{x} (5) + lo g_{x} (5) + 1 - 2.25

Subtract the numbers:

1 - 2.25 = - 1.25

= lo g_{x} (5) + lo g_{x} (5) - 1.25

Apply log rule:

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

lo g_{x} (5) + lo g_{x} (5) = lo g_{x} (5 \cdot 5)

= lo g_{x} (5 \cdot 5) - 1.25

= lo g_{x} (55) - 1.25

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What is log_{x}(sqrt(5))+log_{x}(5x)-2.25 ?
The solution to log_{x}(sqrt(5))+log_{x}(5x)-2.25 is log_{x}(5sqrt(5))-1.25