Question

Rewrite log base 5 of 0.04 = -2 in exponential form.

a) 5⁻² = 0.04
b) 5² = 0.04
c) 5⁻² = 25
d) 5² = 25

Answer 1

The correct exponential form of log base 5 of 0.04 = -2 is 5⁻² = 0.04, which represents that 5 to the power of -2 equals 0.04.

Step-by-step explanation:

To rewrite log base 5 of 0.04 = -2 in exponential form, we interpret the logarithmic statement as the base (5) raised to what power (the right-hand side of the equation, which is -2) equals the number (0.04). Therefore, the exponential form is 5⁻² = 0.04.

This is because logarithms and exponentiation are inverse operations. Raising 5 to the power of -2 means finding the reciprocal of 5 squared. The reciprocal of 5 squared (25) is 1/25, which is equivalent to 0.04. Therefore, 5⁻² = 0.04 is the correct translation of the log equation into exponential form, which aligns with option (a).