Question

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

Answer 1

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Explanation:

Answer 2

`ln((a^(3)b)/(c))`

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((M))/((N))`

`ln(a^(3)b)-ln(c)=ln((a^(3)b)/(c))`

Therefore, our expression as a single logarithm will be
`ln((a^(3)b)/(c))`.