The expression 3lna + ln(b)−ln(c)) written as a single logarithm is In(a³b/c).
What is basic rule of logarithmic?
Product Rule: In(xy) = In(x) + In(y)
Quotient Rule: In(x/y)=In(x) - In(y)
Power Rule: In(xⁿ) = nIn(x)
Given
3Ina + Inb - Inc
Apply the power rule
3Ina + Inb - Inc = Ina³ + Inb - Inc
Apply the product rule
Ina³ + Inb - Inc = In(a³b) - Inc
Apply the quotient rule
In(a³b) - Inc = In(a³b/c)
The expression 3lna + ln(b)−ln(c)) written as a single logarithm is In(a³b/c).
Complete question