SOLUTION: Write the expression as a single natural logarithm. 3 ln 5+2 ln x

Question 392745: Write the expression as a single natural logarithm. 3 ln 5+2 ln x
Answer by jsmallt9(3758) (Show Source): You can put this solution on YOUR website!
3ln(5)+2ln(x)
These are not like terms so we cannot simply add them. But there is a property, , which can be used to combine two logarithms into one. This property requires all of the following:

There is a "+" between the two logarithms. (Note: there is also another property for when there is a "-" between two logarithms.)
The bases of the two logarithms must be the same.
The coefficients of the two logarithms must be 1's.

Your expression meets the first two requirements but not the third one. Fortunately there is another property of logarithms, , which allows us to move a coefficient of a logarithm into its argument as an exponent. Using this property on both of your logarithms we get:

which simplifies to:

Now that the coefficients are 1's we can use the other property to combine the two logarithms:

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