How to solve an equation with the variable as the exponent, 3^(x/2) = 315

The video tutorial explains how to solve the equation X / 2 = 315 by converting it from exponential to logarithmic form. It demonstrates solving for X using the change of base formula and discusses the use of logarithms to eliminate bases. The tutorial concludes with a final calculation to find the value of X, emphasizing the use of base 10 logarithms for calculators that do not support other bases.

What is the first step in converting the equation X / 2 = 315 into logarithmic form?

• Multiply both sides by 2

• Rewrite it as log base 3 of 315

• Divide both sides by 2

• Take the natural logarithm of both sides

Which formula is used to solve logarithms when the calculator does not support log base 3?

• Change of base formula

• Exponential growth formula

• Natural logarithm formula

• Quadratic formula

How do you apply the change of base formula to compute log base 3 of 315?

• Multiply log of 315 by log of 3

• Subtract log of 3 from log of 315

• Divide log of 315 by log of 3

• Add log of 315 to log of 3

What is the purpose of taking the logarithm of both sides of the equation?

• To eliminate the base

• To convert it into exponential form

• To find the exact value of X

• To simplify the equation

What is the final calculated value of X in the equation?

• 11.56

• 10.47

• 9.81

• 12.34