What is ln(x)+(ln(x)-ln(y))/(1-2) ?

The solution to ln(x)+(ln(x)-ln(y))/(1-2) is ln(x)-ln(x/y)

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simplify ln(x)+(ln(x)-ln(y))/(1-2)

simplify

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

ln (x) - ln (\frac{x}{y})

Solution steps

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

Apply log rule:

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

ln (x) - ln (y) = ln (\frac{x}{y})

= ln (x) + \frac{ln ( \frac{x}{y} )}{1 - 2}

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

= ln (x) - ln (\frac{x}{y})

\frac{1}{2} [ln (x) + 2 ln (x + 1)] + 3 ln (x - 5)

lo g_{10} (4 \frac{4 ^{a}}{( a - 4 ) ( 3 a - 4 )})

lo g_{3} (80) \cdot \frac{4}{5}

lo g_{10} (x) + \frac{1}{2} lo g_{10} (y)

lo g_{2} ((2 x - 2)^{2}) - 4 lo g_{2} (1 - x)

What is ln(x)+(ln(x)-ln(y))/(1-2) ?
The solution to ln(x)+(ln(x)-ln(y))/(1-2) is ln(x)-ln(x/y)