What is ln((e*sqrt(x))/(5y^4)) ?

The solution to ln((e*sqrt(x))/(5y^4)) is 1+ln(sqrt(x))-ln(5)-4ln(y)

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simplify ln((e*sqrt(x))/(5y^4))

simplify

ln (\frac{e \cdot x}{5 y ^{4}})

1 + ln (x) - ln (5) - 4 ln (y)

Solution steps

ln (\frac{e x}{5 y ^{4}})

Apply log rule:

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

ln (\frac{e x}{5 y ^{4}}) = ln (e x) - ln (5 y^{4})

= ln (e x) - ln (5 y^{4})

Apply log rule:

lo g_{c} (ab) = lo g_{c} (a) + lo g_{c} (b)

ln (e x) = ln (e) + ln (x), ln (5 y^{4}) = ln (5) + ln (y^{4})

= ln (e) + ln (x) - (ln (y^{4}) + ln (5))

Apply log rule:

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

ln (y^{4}) = 4 ln (y)

= ln (e) + ln (x) - (ln (5) + 4 ln (y))

Apply log rule:

lo g_{a} (a) = 1

= 1 + ln (x) - (4 ln (y) + ln (5))

- (ln (5) + 4 ln (y)) : - ln (5) - 4 ln (y)

= 1 + ln (x) - ln (5) - 4 ln (y)

(0.287) ln (\frac{500}{200}) + (1.05) ln (\frac{680}{980})

ln (\frac{0.42}{- 0.23})

ln (a) - 6 ln (b) + 3 ln (c)

20 lo g_{10} (\frac{4 π}{3 \cdot 1 0 ^{8}})

ln (x^{4}) + ln (x^{5})

What is ln((e*sqrt(x))/(5y^4)) ?
The solution to ln((e*sqrt(x))/(5y^4)) is 1+ln(sqrt(x))-ln(5)-4ln(y)