Combining Logarithms: Simplifying log(a) + 6 log(b)

This article explains how to combine the expression log(a) + 6 log(b) into a single logarithm using the laws of logarithms.

Steps:

Apply the power rule: The coefficient of a logarithm can be moved inside the logarithm as an exponent. Therefore, 6 log(b) becomes log(b^6).
```
log(a) + 6 log(b) = log(a) + log(b^6) 
```
Apply the product rule: Logarithms with the same base that are being added can be combined into a single logarithm where the arguments are multiplied.
```
log(a) + log(b^6) = log(ab^6) 
```

Solution:

The expression log(a) + 6 log(b) can be combined into the single logarithm log(ab^6).