What is 2ln(x-1)+3ln(4)-ln(x) ?

The solution to 2ln(x-1)+3ln(4)-ln(x) is ln((64(x-1)^2)/x)

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simplify 2ln(x-1)+3ln(4)-ln(x)

simplify

2 ln (x - 1) + 3 ln (4) - ln (x)

ln (\frac{64 ( x - 1 ) ^{2}}{x})

Solution steps

2 ln (x - 1) + 3 ln (4) - ln (x)

Apply log rule:

a lo g_{c} (b) = lo g_{c} (b^{a})

2 ln (x - 1) = ln ((x - 1)^{2})

= ln ((x - 1)^{2}) + 3 ln (4) - ln (x)

Apply log rule:

a lo g_{c} (b) = lo g_{c} (b^{a})

3 ln (4) = ln (4^{3})

= ln ((x - 1)^{2}) + ln (4^{3}) - ln (x)

Apply log rule:

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

ln ((x - 1)^{2}) + ln (4^{3}) = ln (4^{3} (x - 1)^{2})

= ln (4^{3} (x - 1)^{2}) - ln (x)

4^{3} = 64

= ln (64 (x - 1)^{2}) - ln (x)

Apply log rule:

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

ln (64 (x - 1)^{2}) - ln (x) = ln (\frac{64 ( x - 1 ) ^{2}}{x})

= ln (\frac{64 ( x - 1 ) ^{2}}{x})

ln (2 \cdot x)

2 π + 16 ln (\frac{2}{2})

- lo g_{10} (5 \times 1 0^{- 4})

lo g_{8} (\frac{8 x ^{2}}{y})

\frac{ln ( 5 )}{ln ( 5 ) - 2 ln ( 3 )}

What is 2ln(x-1)+3ln(4)-ln(x) ?
The solution to 2ln(x-1)+3ln(4)-ln(x) is ln((64(x-1)^2)/x)