i want to know what x is in the logaritme below: 3log x + 2 log 3x= 3 the answer is 3 but how do you get this answer thank you

First, we'll have to precise that we work with decimal
logarithms.

Now, we'll use the power property of
logarithms:

3log x = log
x^3

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

Now, we'll re-write the
equation:

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

Because the bases of logarithms are matching, we'll use
the product property of logarithms: the sum of logarithms is the logarithm of the
product.

 log x^3 + log (3x)^2 = log
[x^3*(3x)^2]

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

We could write the term from the right side
as:

3 = 3*1 = 3* log10

The
equation will become:

log [x^3*(3x)^2] = 3*
log10

log [x^3*(3x)^2] =
log10^3

Because the bases are matching, we'll use the one
to one property:

x^3*(3x)^2 =
1000

9*x^(3+2) = 1000

9x^5 =
1000

We'll divide by 9:

x^5 =
1000/9

x^5 = 111.111 approx.

x
= (111.111)^1/5 approx.