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Popular >

simplify ln(y^{sin(x)}*y)

Solution

simplify

ln (y^{s i n (x)} \cdot y)

Solution

sin (x) ln (y) + ln (y)

Solution steps

ln (y^{s i n (x)} y)

Apply log rule:

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

ln (y^{s i n (x)} y) = ln (y^{s i n (x)}) + ln (y)

= ln (y^{s i n (x)}) + ln (y)

Apply log rule:

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

ln (y^{s i n (x)}) = sin (x) ln (y)

= sin (x) ln (y) + ln (y)

Popular Examples

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

expand (1/2)log_{b}(a)-5log_{b}(c)expand

(\frac{1}{2}) lo g_{b} (a) - 5 lo g_{b} (c)

simplify ln((100+0.11)/(0.11))simplify

ln (\frac{100 + 0.11}{0.11})

simplify ln((0.5)/(1.6))simplify

ln (\frac{0.5}{1.6})

simplify 1/3 ln(49/76)simplify

\frac{1}{3} ln (\frac{49}{76})

Frequently Asked Questions (FAQ)

What is ln(y^{sin(x)}*y) ?
The solution to ln(y^{sin(x)}*y) is sin(x)ln(y)+ln(y)