Question

plify. Assume when necessary that all quant common factors in your final answer. log₈((512)/(x²-196))

Answer 1

To simplify the expression log₈((512)/(x²-196)), we can use the properties of logarithms to rewrite and simplify the expression.

Step-by-step explanation:

To simplify the expression log₈((512)/(x²-196)), we can use the properties of logarithms. First, we can rewrite 512 as 8³, since 512 is a power of 8. Next, we can use the property log(a/b) = log(a) - log(b) to simplify the expression to 3 - log₈(x²-196).

Now, we can further simplify the expression inside the logarithm. We recognize that x²-196 can be factored as (x+14)(x-14). Therefore, we can rewrite the expression as 3 - log₈((x+14)(x-14)).

Finally, we can use the property log(a) + log(b) = log(ab) to simplify the expression to 3 - (log₈(x+14) + log₈(x-14)).