What is ln(8b)-ln(4b)-ln(2)+ln(b) ?

The solution to ln(8b)-ln(4b)-ln(2)+ln(b) is ln(b)

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simplify ln(8b)-ln(4b)-ln(2)+ln(b)

simplify

ln (8 b) - ln (4 b) - ln (2) + ln (b)

ln (b)

Solution steps

ln (8 b) - ln (4 b) - ln (2) + ln (b)

Apply log rule:

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

ln (8 b) - ln (4 b) = ln (\frac{8 b}{4 b})

= ln (\frac{8 b}{4 b}) - ln (2) + ln (b)

\frac{8 b}{4 b} = 2

= ln (2) - ln (2) + ln (b)

Apply log rule:

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

ln (b) - ln (2) = ln (\frac{b}{2})

= ln (2) + ln (\frac{b}{2})

Apply log rule:

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

ln (2) + ln (\frac{b}{2}) = ln (2 \cdot \frac{b}{2})

= ln (2 \cdot \frac{b}{2})

Simplify

2 \cdot \frac{b}{2} : b

= ln (b)

ln (\frac{1050.6}{9.036})

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What is ln(8b)-ln(4b)-ln(2)+ln(b) ?
The solution to ln(8b)-ln(4b)-ln(2)+ln(b) is ln(b)