Question

What is 3lna+lnb−lnc written as a single logarithm?

Answer 1

Answer:

$ln(\frac{a^{3}b}{c})$      

Step-by-step explanation:

We have been given a logarithmic expression and we are asked to write our expression as a single logarithm.

We will Use power, product and quotient rules of logarithm to simplify our given expression.

The power rule of logarithm states that $p\cdot ln(M)=ln(M^{p})$.

$3\cdot ln(a)+ln(b)-ln (c)=ln(a^{3})+ln(b)-ln (c)$  

Now we will use product rule of logarithm, which states that $ln(M)+ln(N)=ln(MN)$.

$ln(a^{3})+ln(b)-ln (c)=ln(a^{3}b)-ln(c)$  

Now let us use quotient rule of logarithm, which states that $ln(M)-ln(N)=ln\frac{(M)}{(N)}$

$ln(a^{3}b)-ln(c)=ln(\frac{a^{3}b}{c})$  

Therefore, our expression as a single logarithm will be $ln(\frac{a^{3}b}{c})$.