Question

Rewrite the logarithmic equation in exponential form: 

Answer 1

First Method:

The function given by f(x) = log_a x is called the logarithmic function with base a.

For x > 0, a > 0, and a ≠ 1,

y = log_a x if and only if x = a^y.

The definition of a logarithm shows an equation written in logarithmic form, y = log_a x, and the same equation written in exponential form x = a^y.

Compare the two equations y = log_a x and  a = log_2/3 9/4 we get,

y = a, x = 9/4 and a = 2/3.

The equation can be written in exponential form as 9/4 = (2/3)^a.

Second method:

The logarithmic equation is .

Exponentiate each side with base 2/3.

Apply inverse property of logarithm : .

The logarithmic equation in exponential form is .

 

Comments

The logarithmic equation in exponential form is (9/4) = (2/3)^a.

(3/2)² = (2/3)^a.

(2/3)^{- 2} = (2/3)^a.

Apply One - to - One property : For a > 0 and a ≠ 1, a^x = a^y ↔ x = y.

- 2 = a.