Question

Drag the tiles to the correct boxes to complete the pairs. Simplify each expression and match it with the equivalent value.

a) ( log_2 64 )
b) ( -log_2 25 )
c) ( log_10 10 )
d) ( log_base unknown 10^4 )

1. ( log_2 64 ) = _______
2. ( -log_2 25 ) = _______
3. ( log_10 10 ) = _______
4. ( log_base unknown 10^4 ) = _______

Answer 1

After simplifying each expression, (log2 64) matches with 6, (log10 10) with 1, and (logbase unknown 104) with 4. There is no exact match for (-log2 25) because 25 is not a power of 2.

Step-by-step explanation:

Let's simplify each logarithmic expression and match it with the equivalent value.

1. ( log2 64 ) = 6 because 26 = 64, so the expression simplifies to 6.
2. ( -log2 25 ) is the negative of the log base 2 of 25. Since 24.64 is approximately 25, the expression is approximately -4.64, but we don't have an exact match since 25 is not a power of 2.
3. ( log10 10 ) = 1 because 101 = 10, simplifying the expression to 1.
4. ( logbase unknown 104 ) assumes the base of the logarithm is 10, so this is simply 4 since 104 = 10000, simplifying to 4.

Hence, the correct pairs would be:

1. ( log2 64 ) = 6
2. ( -log2 25 ) = No exact match since 25 is not a power of 2
3. ( log10 10 ) = 1
4. ( logbase unknown 104 ) = 4