What is log_{5}((25)/(sqrt(x+4))) ?

The solution to log_{5}((25)/(sqrt(x+4))) is 2-log_{5}(sqrt(x+4))

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simplify log_{5}((25)/(sqrt(x+4)))

simplify

lo g_{5} (\frac{25}{x + 4})

2 - lo g_{5} (x + 4)

Solution steps

lo g_{5} (\frac{25}{x + 4})

Apply log rule:

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

lo g_{5} (\frac{25}{x + 4}) = lo g_{5} (25) - lo g_{5} (x + 4)

= lo g_{5} (25) - lo g_{5} (x + 4)

lo g_{5} (25) = 2

= 2 - lo g_{5} (x + 4)

ln (1) - ln (\frac{1}{4})

5 lo g_{10} (x) + 4 lo g_{10} (x - 9)

lo g_{5} (8) - lo g_{5} (x)

2 ln (\frac{3}{2})

What is log_{5}((25)/(sqrt(x+4))) ?
The solution to log_{5}((25)/(sqrt(x+4))) is 2-log_{5}(sqrt(x+4))