SOLUTION: Please help me solve this equation: Solve the logarithmic equation logarithmic equation {{{ log( 2, (ln x) )= -1 }}}. <-- logarithm of lnx(natural log of x) with base 2 equals

Question 309530: Please help me solve this equation:
Solve the logarithmic equation logarithmic equation .
<-- logarithm of lnx(natural log of x) with base 2 equals =-1.
I tried:
.
(log of natural log of x with base 2 equals -1)
.
(natural log of x equals 2 to the power of -1)
.
(natural log of x equals 1/2)
.
(x equals e to the power of 1/2)
I put . back into the original equation and it didn't equal the answer.
Answer by jim_thompson5910(35256) (Show Source): You can put this solution on YOUR website!
Well is the answer.

Start with the given equation.

Plug in

Use the identity to pull down the exponent.

Take the natural log of 'e' to get 1.

Multiply and simplify

Rewrite as

Pull down the exponent using the identity

Evaluate the log base 2 of 2 to get 1.

Multiply

Since the final equation is an identity (ie is always true), this verifies the answer.
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