Question

Use the power property of logarithms to make equivalent statements. log₉(16)=log₉(4)

Answer 1

The power property of logarithms states that if loga(b) = c, then ac = b. Using this property, we can confirm that log9(16) = log9(4) is true and represents equivalent logarithmic statements.

Step-by-step explanation:

The power property of logarithms states that for any positive numbers a, b, and c where a is the base of the logarithm:

• If loga(b) = c, then ac = b.
• If ac = b, then loga(b) = c.

Using this property, we can see that if log9(16) = log9(4), then 9log9(16) = 16 and 9log9(4) = 4. Since 9x always equals x, we can conclude that 16 = 4 in this case. Therefore, the statement log9(16) = log9(4) is true and represents equivalent logarithmic statements.