What is log_{sqrt(2)}(5sqrt(2)) ?

The solution to log_{sqrt(2)}(5sqrt(2)) is 2log_{2}(5)+1

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simplify log_{sqrt(2)}(5sqrt(2))

simplify

lo g_{2} (52)

2 lo g_{2} (5) + 1

Decimal Notation

5.64385 \dots

Solution steps

lo g_{2} (52)

Apply log rule:

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

lo g_{2} (52) = lo g_{2} (5) + lo g_{2} (2)

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

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

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

Apply log rule:

lo g_{a} (a) = 1

lo g_{2} (2) = 1

= 2 lo g_{2} (5) + 1

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cos^{2} (x) - cos (x)

ln (e^{x y})

(x + 7) (x - 7) - (x - 6) (x + 6) + 13

What is log_{sqrt(2)}(5sqrt(2)) ?
The solution to log_{sqrt(2)}(5sqrt(2)) is 2log_{2}(5)+1