Solving Exponential Equations Without Logarithms

The video tutorial covers solving exponential equations without using logarithms. It begins with an introduction to the concept and demonstrates solving equations with exponents that include variables. The tutorial provides multiple examples, illustrating how to manipulate and solve these equations using properties of exponents, such as rewriting numbers as powers of a base, handling negative exponents, and applying the power of a power rule. The video emphasizes solving without a calculator and encourages practice with provided examples.

How can we rewrite the number 1 using a base of 4?

• 4 to the power of 1

• 4 to the power of -1

• 4 to the power of 2

• 4 to the power of 0

What is the solution for x when solving 4^(2x + 3) = 1?

• 3/2

• 2/3

• -2/3

• -3/2

How do we check if our solution for x is correct in an exponential equation?

• Divide the base by x

• Add x to the exponent

• Multiply x by the base

• Substitute x back into the original equation

What rule of exponents do we apply when multiplying expressions with the same base?

• Product of powers rule

• Negative exponent rule

• Power of a power rule

• Quotient of powers rule

What is the solution for x in the equation 4^(-2x) * 4^x = 64?

• -3

• 3

• 2

• -2

How can we represent 1/32 using a base of 2?

• 2 to the power of -4

• 2 to the power of 5

• 2 to the power of 4

• 2 to the power of -5

What is the solution for x when 2^(x - 5) = 2^5?

• 10

• 0

• -10

• 5

When solving exponential equations without a calculator, why is it important to rewrite expressions with the same base?

• To apply the power of a power rule

• To eliminate the variable from the equation

• To simplify the equation using properties of exponents

• To convert the equation into a linear form

What exponent rule is applied when rewriting 1 over a base as a negative exponent?

• Negative exponent rule

• Power of a power rule

• Product of powers rule

• Quotient of powers rule

In the context of exponential equations, what does setting powers equal allow us to solve for?

• The coefficient

• The variable

• The exponent

• The base