What is expand ln((6xsqrt(1+8x))/((x-4)^{13)}) ?

The solution to expand ln((6xsqrt(1+8x))/((x-4)^{13)}) is ln(6)+ln(x)+ln(sqrt(1+8x))-13ln(x-4)

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expand ln((6xsqrt(1+8x))/((x-4)^{13)})

expand

ln (\frac{6 x 1 + 8 x}{( x - 4 ) ^{13}})

ln (6) + ln (x) + ln (1 + 8 x) - 13 ln (x - 4)

Solution steps

ln (\frac{6 x 1 + 8 x}{( x - 4 ) ^{13}})

Apply log rule:

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

ln (\frac{6 x 1 + 8 x}{( x - 4 ) ^{13}}) = ln (6 x 1 + 8 x) - ln ((x - 4)^{13})

= ln (6 x 8 x + 1) - ln ((x - 4)^{13})

Apply log rule:

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

ln ((x - 4)^{13}) = 13 ln (x - 4)

= ln (6 x 1 + 8 x) - 13 ln (x - 4)

Apply log rule:

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

ln (6 x 1 + 8 x) = ln (6) + ln (x) + ln (1 + 8 x)

= ln (6) + ln (x) + ln (8 x + 1) - 13 ln (x - 4)

2 lo g_{10} (x) + 5 lo g_{10} (y)

lo g_{10} (x) + lo g_{10} (x - 3)

2 ln (2) - ln (3)

2 + \frac{1}{2} lo g_{2} (49) - lo g_{2} (21)

ln (7) + ln (x) + ln (y)

What is expand ln((6xsqrt(1+8x))/((x-4)^{13)}) ?
The solution to expand ln((6xsqrt(1+8x))/((x-4)^{13)}) is ln(6)+ln(x)+ln(sqrt(1+8x))-13ln(x-4)