How To Evaluate a Logarithm To a Square Root of a Number Without a Calculator

The video tutorial explains how to simplify logarithmic expressions with different bases, specifically focusing on the case of log base six of the square root of six. It begins by reviewing basic logarithmic properties, such as log base B of B equals one and log base A of A raised to the X equals X. The tutorial then addresses the challenge of having different bases and no exponent, leading to the need to rewrite the square root as a rational exponent. By doing so, the expression can be evaluated using known logarithmic properties, resulting in a simplified form.

What is the result of log base B of B?

• Undefined

• B

• 1

• 0

If you have log base a of a raised to the X, what does it simplify to?

• a

• X

• 1

• a^X

Why can't the expression log base six of sqrt 6 be directly simplified to the square root?

• Because it is an irrational number

• Because it is a complex number

• Because it is already simplified

• Because the bases are not the same

How can the square root be expressed to use logarithmic properties?

• As a whole number

• As a decimal

• As a fraction

• As a rational exponent

What is the final evaluated result of log base six of six raised to the 1/2 power?

• 1

• 1/2

• 6

• sqrt 6