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Popular >

simplify ln(y/x e^t)

Solution

simplify

ln (\frac{y}{x} e^{t})

Solution

ln (y) - ln (x) + t

Solution steps

ln (\frac{y}{x} e^{t})

Apply log rule:

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

ln (\frac{y}{x} e^{t}) = ln (\frac{y}{x}) + ln (e^{t})

= ln (\frac{y}{x}) + ln (e^{t})

Apply log rule:

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

ln (e^{t}) = t ln (e)

= ln (\frac{y}{x}) + t ln (e)

Apply log rule:

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

ln (\frac{y}{x}) = ln (y) - ln (x)

= ln (y) - ln (x) + ln (e) t

t ln (e) = t

= ln (y) - ln (x) + t

Popular Examples

simplify-2ln(1/4)simplify

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

simplify ln(4e^y)simplify

ln (4 e^{y})

join 2log_{3/7}(7)join

2 lo g_{\frac{3}{7}} (7)

simplify ln(0.02sqrt(1-0.9^2))simplify

ln (0.02 1 - 0. 9^{2})

simplify (ln(20)-ln(40))/(-0.3)simplify

\frac{ln ( 20 ) - ln ( 40 )}{- 0.3}

Frequently Asked Questions (FAQ)

What is ln(y/x e^t) ?
The solution to ln(y/x e^t) is ln(y)-ln(x)+t