What is ln(c)-ln(d)+ln(0.017+c)-ln(0.017-d) ?

The solution to ln(c)-ln(d)+ln(0.017+c)-ln(0.017-d) is ln((c(0.017+c))/(d(0.017-d)))

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simplify ln(c)-ln(d)+ln(0.017+c)-ln(0.017-d)

simplify

ln (c) - ln (d) + ln (0.017 + c) - ln (0.017 - d)

ln (\frac{c ( 0.017 + c )}{d ( 0.017 - d )})

Solution steps

ln (c) - ln (d) + ln (0.017 + c) - ln (0.017 - d)

Apply log rule:

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

ln (c) - ln (d) = ln (\frac{c}{d})

= ln (\frac{c}{d}) + ln (0.017 + c) - ln (0.017 - d)

Apply log rule:

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

ln (\frac{c}{d}) + ln (0.017 + c) = ln (\frac{c}{d} (c + 0.017))

= ln (\frac{c}{d} (c + 0.017)) - ln (- d + 0.017)

Multiply fractions:

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

= ln (\frac{c ( 0.017 + c )}{d}) - ln (0.017 - d)

Apply log rule:

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

ln (\frac{c ( 0.017 + c )}{d}) - ln (0.017 - d) = ln (\frac{\frac{c ( c + 0.017 )}{d}}{- d + 0.017})

= ln (\frac{\frac{c ( 0.017 + c )}{d}}{0.017 - d})

Apply the fraction rule:

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

= ln (\frac{c ( 0.017 + c )}{d ( 0.017 - d )})

ln (\frac{x ( x ^{6} + 23 )}{x ^{3} + x - 2})

lo g_{b} (\frac{3 x ^{2}}{b ^{2}})

lo g_{4} (\frac{y ^{8}}{16 x})

6 lo g_{5} (x) + 2 lo g_{5} (4 x) - \frac{1}{5} lo g_{5} (4 - x)

lo g_{x} (\frac{yz}{w})

What is ln(c)-ln(d)+ln(0.017+c)-ln(0.017-d) ?
The solution to ln(c)-ln(d)+ln(0.017+c)-ln(0.017-d) is ln((c(0.017+c))/(d(0.017-d)))