What is log_{5}((e^x)/(x^{1/2)}) ?

The solution to log_{5}((e^x)/(x^{1/2)}) is xlog_{5}(e)-1/2 log_{5}(x)

Popular >

simplify log_{5}((e^x)/(x^{1/2)})

simplify

lo g_{5} (\frac{e ^{x}}{x ^{\frac{1}{2}}})

x lo g_{5} (e) - \frac{1}{2} lo g_{5} (x)

Solution steps

lo g_{5} (\frac{e ^{x}}{x ^{\frac{1}{2}}})

Apply log rule:

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

lo g_{5} (\frac{e ^{x}}{x ^{\frac{1}{2}}}) = lo g_{5} (e^{x}) - lo g_{5} (x^{\frac{1}{2}})

= lo g_{5} (e^{x}) - lo g_{5} (x^{\frac{1}{2}})

Apply log rule:

lo g_{a} (x^{b}) = b \cdot lo g_{a} (x)

lo g_{5} (e^{x}) = x lo g_{5} (e)

= x lo g_{5} (e) - lo g_{5} (x^{\frac{1}{2}})

Apply log rule:

lo g_{a} (x^{b}) = b \cdot lo g_{a} (x)

lo g_{5} (x^{\frac{1}{2}}) = \frac{1}{2} lo g_{5} (x)

= x lo g_{5} (e) - \frac{1}{2} lo g_{5} (x)

2.5 \cdot ln (\frac{70}{50}) - 0.8

- ln ∣ x - 2 ∣ + 4 ln ∣ x + 5 ∣ + C

ln (\frac{4}{x})

8 lo g_{10} (c) + 8 lo g_{10} (a) - 4 lo g_{10} (b)

ln (cos (x)) - ln (cos (y))

What is log_{5}((e^x)/(x^{1/2)}) ?
The solution to log_{5}((e^x)/(x^{1/2)}) is xlog_{5}(e)-1/2 log_{5}(x)