Question

HW-13-Properties-of-Logs Section 3.2: Pr

Let L(x)=logₐ(x) where we don't know the base
a. However, we do know that L(2)=0.27272 Then a

Answer 1

To find the base 'a' of the logarithmic function L(x)=log_a(x) with L(2)=0.27272, we solve the equation a^0.27272 = 2, resulting in a being raised to the reciprocal of 0.27272.

Step-by-step explanation:

The question asks about the properties of logarithms, specifically if the logarithmic function L(x)=log_a(x) yields a value of 0.27272 when evaluated at x=2. We can use this information to find the unknown base 'a' of the logarithm. Remembering that the logarithmic function represents the exponent that the base 'a' must be raised to in order to yield 'x', we can set up an equation a^0.27272 = 2 to solve for 'a'. Using a calculator or a logarithmic identity, we can find the value of 'a' by raising the number 2 to the power of 1/0.27272.