Question

Which of the following expressions are equivalent? (Select all that are correct).

a) log₇ 10 = x and 7 = 10
b) log₅₅ 1 = x and 1⁵⁵ = x
c) log₁₀ 10 = x and 10¹⁰ = x
d) log₁₀ 3 = x and 10 = 3

Answer 1

The correct expressions are: a) log₇ 10 = x and 7 = 10, c) log₁₀ 10 = x and 10¹⁰ = x. The other expressions are not equivalent.

Step-by-step explanation:

The correct expressions are:

• a) log₇ 10 = x and 7 = 10
• c) log₁₀ 10 = x and 10¹⁽ = x

In these expressions, we can see that the logarithm of 10 to base 7 or 10 is equal to x. This means that 7 raised to the power of x is equal to 10, or 10 raised to the power of x is equal to 10.

The other expressions are not equivalent because they do not satisfy the same relationship between the logarithm and the exponent.