#6. Condense the expression to the logarithmic of a single quanity.
[2log 5 (x+4)+7log 5 (x+7)]-1/2log 5 x
Use the properties of logs.
1. Sketch the graph of the function:
You're expected to be familiar with the graph of .
This is the same graph translated up 3 units.
2. Evaluate the expression without using a calculator:
Rewrite in exponential form: .
Get the same base on both sides: .
Since the bases are equal, the exponents are equal: .
3. Identify the logarithmic equation written in exponential form:
Not sure what "identify" means here . . .
In exponential form, the expression is: .
4. Evaluate using the change-of-base formula:
We have: .
5. Which is the logarithm rewritten as a ratio of natural logarithms?
. . .
Is there a typo? . . . Both and are ratios of natural logs.
6. Condense the expression to the logarithm of a single quantity:
. . .