Condense each expression to a single logarithm.: 8 log2 x + 2 log2 y

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mariloucortez | High School Teacher | (Level 3) Adjunct Educator

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Use the properties:

`nlog_b a = log_b a^n`


`log_b a + log_b c = log_b(ac)`

Notice that terms should have the same bases (the small number beside log) to apply the properties.

Start with the use of the first property above:

`8log_2 x`

n = 8, b = 2 and a = x

`8log_2 x = log_2 x^8`

Do the same with the second term.

`2log_2 y`

n = 2, b = 2, and a = y

`2log_2 y = log_2 y^2`

So, you have `log_2x^8 + log_2y^2`

Then, use the second property.

b = 2, a = x^8 and c = y^2

`log_2x^8 + log_2y^2 = log_2(x^8 * y^2)`

Thus, the answer is `log_2 x^8y^2.`


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