What is ln(x)-(ln(ln(y/x))-ln(y/x)) ?

The solution to ln(x)-(ln(ln(y/x))-ln(y/x)) is ln(y/(ln(y/x)))

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simplify ln(x)-(ln(ln(y/x))-ln(y/x))

simplify

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

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

Solution steps

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

Apply log rule:

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

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

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

Apply the fraction rule:

\frac{a}{\frac{b}{c}} = \frac{a \cdot c}{b}

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

Apply log rule:

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

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

= ln \frac{x}{\frac{x l n ( \frac{y}{x} )}{y}}

Simplify

\frac{x}{\frac{x l n ( \frac{y}{x} )}{y}} : \frac{y}{ln ( \frac{y}{x} )}

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

2 ln (\frac{1}{0.96})

20 e^{3 (3)} - ln (3 + 9) - 20 e^{3 (0)} - ln (0 + 9)

ln (\frac{66}{58})

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

- \frac{1}{3} ln 1 - 3 v^{2} - ln ∣ x ∣

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