Question

Condense each expression to a single logarithm. log₈b+5log₈c+(log_₈a)/(3) Solve each equation. Give your answer as a fraction

Answer 1

The expression log₈b + 5log₈c + (log_₈a)/3 can be condensed to a single logarithm using properties of logarithms to get the condensed form log₈(bc⁵a^(1/3)).

Step-by-step explanation:

To condense the expression log₈b + 5log₈c + (log_₈a)/3 to a single logarithm, we use the properties of logarithms. Specifically, the properties that state the logarithm of a product is the sum of the logarithms, and the logarithm of a power is the exponent times the logarithm.

By applying these properties, we can rewrite the expression as follows:

1. Move the coefficient 5 in front of log₈c to the exponent position: log₈b + log₈c⁵.
2. Move the 1/3 coefficient in front of log₈a to the exponent position: log₈b + log₈c⁵ + log₈a^(1/3).
3. Combine the three logarithms using the property log x + log y = log(xy): log₈(bc⁵a^(1/3)).

Therefore, the condensed expression is log₈(bc⁵a^(1/3)).