The exponential equation 8x=480

Question

does not have an integer solution, yet the solution does lie between two integer values. Use a calculator to fill in the blanks of the following statement with the two integer values that x must lie between.

Hint: Put the smaller number in the first response field and the larger number in the second response field.

(1 point)
The number 8 must be raised to a power between the numbers
and
to equal the value of 480.

Answer 1

To find the values between which x must lie, we can use logarithms. Taking the logarithm of both sides of the equation, we have:

log(8x) = log(480)

Using the property of logarithms that states log(a^b) = b*log(a), we can rewrite the equation as:

x*log(8) = log(480)

Now, using a calculator:

x = log(480)/log(8) ≈ 2.760

Since x must be an integer, it must lie between 2 and 3.

So, the solution lies between the numbers 2 and 3.