Question

Solve for x if .5^x=128

Answer 1

x = -7

Explanation:

We can solve for x using the following steps:

Step 1: Take the log of both sides:

log (0.5^x) = log (128)

Step 2: Apply the power rule of logs and bring down x:

x * log (0.5) = log (128)

Step 3: Divide both sides by log (0.5) to solve for x:

x = (log (128) / log (0.5))

x = -7

Therefore, x = -7.

Answer 2

x ≈ -7. Solved using log base 0.5 and change of base formula.

Here's how to solve for x in 0.5^x = 128:

Step 1: Take the logarithm of both sides.

We can use logarithms to get rid of the exponent. Here, we want to isolate x, so we need to take the log base 0.5 of both sides:

log0.5(0.5^x) = log0.5(128)

2: Simplify the equation.

Using the property log_a(a^x) = x, the left side simplifies to x. The right side can be rewritten using the change of base formula:

x = log(128) / log(0.5)

3: Calculate the result.

You can use a calculator to find the value of the expression. Using the approximate values:

x ≈ 2.1072 / -0.3010 ≈ -7

Therefore, the solution to the equation 0.5^x = 128 is x ≈ -7.

Question:

How do I solve for x in 0.5^x = 128?