Question

The number of subscribers to a streaming video service doubles each week.

Answer 1

Answer:

Step-by-step explanation:

This is an exponential equation that is solved by taking the natural log of both sides.  The equation is

$f(x)=2^x$

If we are looking for x when f(x) = 64, then

$64=2^x$

Take the natural log of both sides:

$ln(64)=ln(2^x)$

The rules of logs allows us to bring the x down in front:

$ln(64)=xln(2)$

Divide both sides by ln(2) to get:

$\frac{ln(64)}{ln(2)}=x$

Do this on your calculator to get that x = 6.

You could also have just gone right to your calculator and started raising 2 to consecutive powers starting at like 3 or 4 to eventually get that 2 to the 6th power is equal to 64, but for the basics of solving log equations, you need to know how to do this.

Answer 2

Answer:

A. $\displaystyle Week\:6$

Step-by-step explanation:

$\displaystyle 64 = 2^x \\ \\ log_264 = x; 6 = x$

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