Solving Exponential Equations

The video tutorial explains how to solve the exponential equation 6^x = 10 using logarithms. It covers isolating the exponential part, converting the equation to logarithmic form, and finding a decimal approximation using the change of base formula. The solution is verified through substitution and graphical methods, ensuring accuracy. The tutorial provides step-by-step instructions and multiple methods for entering equations and checking solutions.

What is the first step in solving the exponential equation 6^x = 10?

• Use the quadratic formula

• Find a common base

• Isolate the exponential part

• Directly convert to a logarithm

Which key combination is used to enter the exponent in the equation 6^x = 10 using a keyboard?

• Shift + 5

• Alt + 5

• Shift + 6

• Ctrl + 6

In the equation 6^x = 10, what is the base when converting to logarithmic form?

• x

• 10

• None of the above

• 6

What is the logarithmic form of the equation 6^x = 10?

• x = log_x(6)

• x = log_6(10)

• x = log_10(6)

• x = log_6(x)

Which formula is used to find a decimal approximation of the solution?

• Pythagorean theorem

• Quadratic formula

• Change of base formula

• Binomial theorem

What is the decimal approximation of x to three decimal places for the equation 6^x = 10?

• 1.300

• 1.250

• 1.295

• 1.285

How can you verify the solution by substitution?

• Check if 6^1.285 is greater than 10

• Check if 6^1.285 is less than 10

• Check if 6^1.285 is approximately 10

• Check if 6^1.285 is exactly 10

What is the graphical method to verify the solution?

• Plot y = 6^x and y = x and find the intersection

• Plot y = 6^x and y = 10 and find the intersection

• Plot y = x^6 and y = 10 and find the intersection

• Plot y = 10^x and y = 6 and find the intersection

What should be adjusted in the graph to better view the intersection point?

• Increase the X maximum

• Decrease the Y maximum

• Decrease the X minimum

• Increase the Y maximum

What is the approximate x-coordinate of the intersection point on the graph?

• 1.300

• 1.295

• 1.250

• 1.285