Question

Condense each expression to a single logarithm.

Answer 1

To condense the log expressions, we apply properties of logarithms, combining them by multiplication and division into single logarithms: for the first, log_5(7· 8· 3^5); for the second,
`log_6\left((x^2)/(y^6)\right).`

To condense each expression to a single logarithm, we use properties of logarithms such as log(x) + log(y) = log(xy), and n·log(x) = log(x^n).

For the first expression, we can combine the logarithms by multiplication:

log_57 + log_5 8 + 5·log_5 3 = log_5(7· 8· 3^5)

Now, let's simplify the second expression using division and exponentiation:

`2·log_6 x - 6·log_6 y = log_6(x^2) - log_6(y^6) = log_6\left((x^2)/(y^6)\right)`

The probable question may be:

Condense each expression to a single logarithm.

1. log_57+log_5 8+5 log_5 3

2. 2 log_6 x-6 log_6 y