Rewriting Logarithms

• 6

• 3

• 5

• 4

Answer explanation

To expand the logarithmic expression log_2(8), we need to find the power to which the base 2 must be raised to get 8. 2^3 = 8, so log_2(8) = 3.

Tags

CCSS.HSF.BF.B.5

• e^ln(3)

• 3^e

• 3

• ln(3)

Answer explanation

The natural logarithm ln(e^3) simplifies to 3 because the natural logarithm and exponential functions are inverse operations, canceling each other out.

Tags

CCSS.HSF.BF.B.5

• 5

• 0

• 2

• -1

Answer explanation

To expand log(base 5) (25/125), we can rewrite it as log(base 5) (25) - log(base 5) (125). This simplifies to 2 - 3 = -1.

Tags

CCSS.HSF.BF.B.5

• 81

• 3

• 1

• 9

Answer explanation

To expand the logarithmic expression log(base 3) (27^(1/3)), we use the property log(base a) (a^b) = b. Therefore, log(base 3) (27^(1/3)) = 1.

Tags

CCSS.HSF.BF.B.5

• 8

• 4

• 16

• 1

Answer explanation

To expand the logarithmic expression log(base 4) (2^2), we use the property log(base a) (b) = c, where a^c = b. Therefore, 4^1 = 2^2, so the answer is 1.

Tags

CCSS.HSF.BF.B.5

• 5

• 2

• 4

• 3

Answer explanation

To condense the expression, use the property of logarithms: log(a) - log(b) = log(a/b). Therefore, log(base 6) 216 - log(base 6) 6 = log(base 6) (216/6) = log(base 6) 36 = 2.

Tags

CCSS.HSF.BF.B.5

Answer explanation

To condense the expression, use the rule log(a) - log(b) = log(a/b). Therefore, 2log(base 3) x - log(base 3) y = log(base 3) (x^2/y).

Tags

CCSS.HSA.SSE.A.2

CCSS.HSA.SSE.B.3

CCSS.HSF.IF.C.8

Answer explanation

Choose the correct answer choice: log(base 2) (a * b) combines the logarithms of a and b with addition, resulting in log(base 2) (a * b).

Tags

CCSS.HSA.SSE.B.3

CCSS.HSF.BF.B.5

CCSS.HSF.IF.C.8

Answer explanation

Choose the answer that condenses the logarithmic expression correctly by combining like terms. In this case, the correct choice is log(base 5) (x^3 / y^2).

Tags

CCSS.HSA.SSE.A.2

CCSS.HSA.SSE.B.3

CCSS.HSF.BF.B.5

CCSS.HSF.IF.C.8

Answer explanation

Choose the option that combines the logarithmic terms by adding them together: log(base 7) (x^2y^3)

Tags

CCSS.HSA.SSE.A.2

CCSS.HSA.SSE.B.3

CCSS.HSF.BF.B.5

CCSS.HSF.IF.C.8