Question

Klay, needs to answer the given logarithmic equation on the board, the given; log5(x + 2) = 3. What value of x should Klay answer?

Answer 1

To solve the logarithmic equation log5(x + 2) = 3, rewrite it in exponential form to get 5^3 = x + 2. Calculate 5^3 to get 125 and then subtract 2 to find that Klay should answer x = 123.

Step-by-step explanation:

The student wants to solve the logarithmic equation log5(x + 2) = 3. To solve for x, you need to rewrite the equation in its exponential form: 53 = x + 2. Once you have this, calculate 5 raised to the power of 3 and then subtract 2 from the result to find the value of x.

First, calculate 53:

• 53 = 5 × 5 × 5
• 53 = 125

Then, subtract 2:

• 125 - 2 = 123

Therefore, the value of x that Klay should answer is 123.

The exponential form and logarithm rules are crucial concepts in solving this problem. Understanding that the logarithm of a number raised to an exponent is the product of the exponent and the logarithm of the number is pivotal. In this particular equation, it is applied in reverse; by raising the base of the logarithm (5) to the power on the other side of the equation (3), we are able to solve for x.