Question 1

Expand the expression $$\log_{25}(25xy) as $$much as possible into a sum or difference of logarithms.

Accepted Answer

$$\log_{25}(25) + \log_{25}(x) + \log_{25}(y)$$

Question 2

Expand the expression $$\log_{4}\left(\frac{7}{x^2$}\right) as $$much as possible into a sum or difference of logarithms.

Accepted Answer

$$\log_{4}(7) - 2\log_{4}(x)$$

Question 3

Expand the expression $$\log_{5}\left(\frac{y}{4x}\right) as $$much as possible into a sum or difference of logarithms.

Accepted Answer

$$\log_{5}(y) - \log_{5}(4) - \log_{5}(x)$$

Question 4

Expand the expression $$\log_{10}(100x^2$) as $$much as possible into a sum or difference of logarithms.

Accepted Answer

$$\log_{10}(100) + \log_{10}(x^2$)$$

Question 5

Expand the expression $$\ln(x^2$ \cdot \sqrt{x+3}) as $$much as possible into a sum or difference of logarithms.

Accepted Answer

$$2\ln(x) + \frac{1}{2}\ln(x+3)$$

Expanding Logarithmic Expressions: Sums and Differences

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