Question

Expand the expression log(8x/5) using the properties of logarithms.(1 point) Responses 8logx−log5 8 logarithm x minus logarithm 5 log8+logx−log5 logarithm 8 plus logarithm x minus logarithm 5 log8⋅logxlog5 Start Fraction logarithm 8 times logarithm x over logarithm 5 End Fraction log8+logx

Answer 1

To expand the expression \( \log\left(\frac{8x}{5}\right) \) using the properties of logarithms, we can use the following logarithmic identities:

1. \( \log\left(\frac{a}{b}\right) = \log a - \log b \) (the logarithm of a quotient)
2. \( \log(ab) = \log a + \log b \) (the logarithm of a product)

Applying these properties:

\[
\log\left(\frac{8x}{5}\right) = \log(8x) - \log(5)
\]

Now, we can further break down \( \log(8x) \):

\[
\log(8x) = \log(8) + \log(x)
\]

Putting it all together, we have:

\[
\log\left(\frac{8x}{5}\right) = \log(8) + \log(x) - \log(5)
\]

The expanded form is:

\[
\log(8) + \log(x) - \log(5)
\]

So, the correct response is **log8 + logx - log5**.