Answer:
[tex]ln(\frac{a^{3}b}{c})[/tex]
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 [tex]p\cdot ln(M)=ln(M^{p})[/tex].
[tex]3\cdot ln(a)+ln(b)-ln (c)=ln(a^{3})+ln(b)-ln (c)[/tex]
Now we will use product rule of logarithm, which states that [tex]ln(M)+ln(N)=ln(MN)[/tex].
[tex]ln(a^{3})+ln(b)-ln (c)=ln(a^{3}b)-ln(c)[/tex]
Now let us use quotient rule of logarithm, which states that [tex]ln(M)-ln(N)=ln\frac{(M)}{(N)}[/tex]
[tex]ln(a^{3}b)-ln(c)=ln(\frac{a^{3}b}{c})[/tex]
Therefore, our expression as a single logarithm will be [tex]ln(\frac{a^{3}b}{c})[/tex].
