What is log_{e}(x)+1-log_{e}(5) ?

The solution to log_{e}(x)+1-log_{e}(5) is ln(x/5)+1

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simplify log_{e}(x)+1-log_{e}(5)

simplify

lo g_{e} (x) + 1 - lo g_{e} (5)

ln (\frac{x}{5}) + 1

Solution steps

lo g_{e} (x) + 1 - lo g_{e} (5)

Apply log rule:

lo g_{c} (a) - lo g_{c} (b) = lo g_{c} (\frac{a}{b})

lo g_{e} (x) - lo g_{e} (5) = lo g_{e} (\frac{x}{5})

= lo g_{e} (\frac{x}{5}) + 1

Apply log rule:

lo g_{e} (x) = ln (x)

= ln (\frac{x}{5}) + 1

ln (\frac{1}{3 ^{2}})

25 ln (25) - 16 ln (16) - 9 ln (e)

ln (\frac{2}{16})

lo g_{10} (\frac{8}{3 ^{2}})

- ln (x) + ln^{2} (x)

What is log_{e}(x)+1-log_{e}(5) ?
The solution to log_{e}(x)+1-log_{e}(5) is ln(x/5)+1