What is ln((5xsqrt(1+3x))/((x-3)^7)) ?

The solution to ln((5xsqrt(1+3x))/((x-3)^7)) is ln(5)+ln(x)+ln(sqrt(1+3x))-7ln(x-3)

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simplify ln((5xsqrt(1+3x))/((x-3)^7))

simplify

ln (\frac{5 x 1 + 3 x}{( x - 3 ) ^{7}})

ln (5) + ln (x) + ln (1 + 3 x) - 7 ln (x - 3)

Solution steps

ln (\frac{5 x 1 + 3 x}{( x - 3 ) ^{7}})

Apply log rule:

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

ln (\frac{5 x 1 + 3 x}{( x - 3 ) ^{7}}) = ln (5 x 1 + 3 x) - ln ((x - 3)^{7})

= ln (5 x 3 x + 1) - ln ((x - 3)^{7})

Apply log rule:

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

ln ((x - 3)^{7}) = 7 ln (x - 3)

= ln (5 x 1 + 3 x) - 7 ln (x - 3)

Apply log rule:

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

ln (5 x 1 + 3 x) = ln (5) + ln (x) + ln (1 + 3 x)

= ln (5) + ln (x) + ln (3 x + 1) - 7 ln (x - 3)

- \frac{1}{4} ln (3)

4.74 + lo g_{10} (\frac{0.0105}{0.0095})

ln (47 e^{x t})

lo g_{6} (u) + 6 lo g_{6} (v)

\frac{ln ( \frac{125}{4} )}{3 ln ( 2 )}

What is ln((5xsqrt(1+3x))/((x-3)^7)) ?
The solution to ln((5xsqrt(1+3x))/((x-3)^7)) is ln(5)+ln(x)+ln(sqrt(1+3x))-7ln(x-3)