Exponents and Logarithmic Equations

The video tutorial explains how to evaluate logarithmic expressions without using a calculator. It covers converting logarithmic equations into exponential form to find the value of x. Examples include solving log base 5 of 0.008, log base 10 of 0.001, log base 625 of the square root of 5, and log base 4 of 32. The tutorial emphasizes writing both sides of the equation with the same base and using prime factorization to simplify expressions.

What is the first step in evaluating a logarithmic expression without a calculator?

• Convert the expression to a fraction

• Set the expression equal to a variable

• Guess the value of the expression

• Use a calculator to find the value

In the example of log base 5 of 0.008, what is the equivalent exponential equation?

• 5^x = 8

• 5^x = 0.008

• 5^x = 0.8

• 5^x = 0.08

What is the value of x in the equation 5^x = 1/125?

• x = -3

• x = 3

• x = 1/3

• x = -1/3

How is 0.001 expressed as a power of 10?

• 10^-3

• 10^0.001

• 10^1

• 10^3

What is the value of x in the equation 10^x = 0.001?

• x = 1/3

• x = -1/3

• x = -3

• x = 3

What is the prime factorization of 625?

• 5^2

• 5^5

• 5^4

• 5^3

How can the square root of 5 be expressed using exponents?

• 5^3

• 5^2

• 5^1

• 5^0.5

What is the value of x in the equation 625^x = √5?

• x = 1/4

• x = 1/8

• x = 1/2

• x = 1/16

How is 32 expressed as a power of 2?

• 2^4

• 2^5

• 2^3

• 2^6

What is the value of x in the equation 4^x = 32?

• x = 5/2

• x = 3/2

• x = 2/5

• x = 5