Question

2log3 of 3 + log3 of 5 = log3 of x

How would I add it up?

Would it be like this: 2log3 of (3/5) = log3 of x

Answer 1

No, but close.
You can't apply this rule:\[\Large\rm \log(a)+\log(b)=\log(ab)\]While there is a 2 sitting in front of the first log.
That's causing a problem for us.

Answer 2

Remember this rule?\[\Large\rm b\cdot \log(a)=\log(a^b)\]

Answer 3

Are you trying to write as a single logarithmic expression

Answer 4

I need it applied to the problem not just give me the property

Answer 5

it is easy to write the sum of logarithms as a single term, since the bases are matching and we could apply the product rule.

But before applying the product rule, we'll have to apply the power rule of logarithms for the term 2*log 3 x:

2*log 3 x = log 3 (x^2)

We'll re-write the expression:

2 log3 x + log3 5 = log 3 (x^2) + log3 5

Now, we can apply the product rule:

log a x + log a y = log a(x*y)

We'll put a = 3:

log 3 (x^2) + log3 5 = log 3 (5*x^2)

The simplified logarithmic term is:log 3 (5*x^2)

Answer 6

Understand?

Answer 7

@here_to_help15 wouldn't it be x over 2 (x/2) why is it x^2

Answer 8

power rule !
\[\huge\rm log_b y^2 \] \[\rm \color{red}{2 \log_b y} \]