Question

How can you use a logarithmic function to solve 8^x=32,768 ? Choose all of the statements that apply.

A. 8ˣ=32,768 is equivalent to x=log _832, 768=5.
B. 8ˣ=32, 768 is equivalent to x=log _532,768=8.
C. Logarithms are inverse functions to exponential functions.
D. Logarithms are equal to exponential functions.
E、 8ˣ=32,768 is equivalent to x= (log 32,768)/log 8 =5.

Answer 1

To solve the equation 8 to the power of x equals 32,768, we can apply logarithms to both sides, use logarithmic properties to isolate x, and calculate the resulting values to find that x equals 5.

Step-by-step explanation:

To solve the exponential equation 8x = 32,768 using logarithms, we convert the equation into logarithmic form. This is because logarithms are the inverse functions to exponential functions, allowing us to solve for the exponent. This process involves applying the logarithm on both sides of the equation and using the property that the logarithm of a number raised to an exponent is the product of the exponent and the logarithm of the number.

The correct steps for solving the equation using logarithms are:

1. Apply logarithms to both sides of the equation: log(8x) = log(32,768).
2. Use the property of logarithms to bring down the exponent: x • log(8) = log(32,768).
3. Solve for x: x = (log 32,768) / (log 8).
4. Calculate the values: x = 5, since 85 is indeed equal to 32,768.

Therefore, the correct statements from the given options are:

• C. Logarithms are inverse functions to exponential functions.
• E. 8x = 32,768 is equivalent to x = (log 32,768)/(log 8) = 5.