What is ln(x)-(ln(y)+ln(z))-2ln(a) ?

The solution to ln(x)-(ln(y)+ln(z))-2ln(a) is ln(x/(a^2yz))

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simplify ln(x)-(ln(y)+ln(z))-2ln(a)

simplify

ln (x) - (ln (y) + ln (z)) - 2 ln (a)

ln (\frac{x}{a ^{2} yz})

Solution steps

ln (x) - (ln (y) + ln (z)) - 2 ln (a)

Apply log rule:

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

2 ln (a) = ln (a^{2})

= ln (x) - (ln (y) + ln (z)) - ln (a^{2})

Apply log rule:

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

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

= ln (\frac{x}{a ^{2}}) - (ln (y) + ln (z))

Apply log rule:

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

ln (y) + ln (z) = ln (yz)

= ln (\frac{x}{a ^{2}}) - ln (yz)

Apply log rule:

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

ln (\frac{x}{a ^{2}}) - ln (yz) = ln (\frac{\frac{x}{a ^{2}}}{yz})

= ln (\frac{\frac{x}{a ^{2}}}{yz})

Apply the fraction rule:

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

= ln (\frac{x}{a ^{2} yz})

lo g_{8} (3 x^{4})

lo g_{8} (x^{3})

ln (\frac{4.7926}{- 4.92})

lo g_{7} ((a^{4} b)^{4})

lo g_{5} (8 \frac{t}{v})

What is ln(x)-(ln(y)+ln(z))-2ln(a) ?
The solution to ln(x)-(ln(y)+ln(z))-2ln(a) is ln(x/(a^2yz))