What is ln((6xsqrt(1+4x))/((x-3)^9)) ?

The solution to ln((6xsqrt(1+4x))/((x-3)^9)) is ln(6)+ln(x)+ln(sqrt(1+4x))-9ln(x-3)

Popular >

simplify ln((6xsqrt(1+4x))/((x-3)^9))

simplify

ln (\frac{6 x 1 + 4 x}{( x - 3 ) ^{9}})

ln (6) + ln (x) + ln (1 + 4 x) - 9 ln (x - 3)

Solution steps

ln (\frac{6 x 1 + 4 x}{( x - 3 ) ^{9}})

Apply log rule:

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

ln (\frac{6 x 1 + 4 x}{( x - 3 ) ^{9}}) = ln (6 x 1 + 4 x) - ln ((x - 3)^{9})

= ln (6 x 4 x + 1) - ln ((x - 3)^{9})

Apply log rule:

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

ln ((x - 3)^{9}) = 9 ln (x - 3)

= ln (6 x 1 + 4 x) - 9 ln (x - 3)

Apply log rule:

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

ln (6 x 1 + 4 x) = ln (6) + ln (x) + ln (1 + 4 x)

= ln (6) + ln (x) + ln (4 x + 1) - 9 ln (x - 3)

ln (0.5 \cdot c^{0.5} \cdot z^{0.5})

ln (\frac{2 x}{5})

- \frac{5}{4} ln (\frac{0.01}{0.9})

\frac{300}{2 \cdot π \cdot 1200} \cdot ln (\frac{4 + 2 \cdot 120 0 ^{2}}{25})

\frac{- 5 ln ( 5 ) - 4 ln ( 2 )}{7 ln ( 5 ) - ln ( 2 )}

What is ln((6xsqrt(1+4x))/((x-3)^9)) ?
The solution to ln((6xsqrt(1+4x))/((x-3)^9)) is ln(6)+ln(x)+ln(sqrt(1+4x))-9ln(x-3)