Solve algebraically. Round to the nearest thousandth.

Question

ln(5−2^x)=0

Answer 1

To solve this equation algebraically, we first need to isolate the exponent term:

ln(5 - 2^x) = 0
5 - 2^x = e^0
5 - 2^x = 1

Next, we isolate the exponent term by subtracting 5 from both sides:

-2^x = 1 - 5
-2^x = -4

Now, we divide both sides by -2 to solve for x:

2^x = 4

Taking the natural logarithm of both sides to isolate the exponent:

ln(2^x) = ln(4)
x * ln(2) = ln(4)

Now, divide both sides by ln(2) to solve for x:

x = ln(4) / ln(2)
x ≈ 2

Therefore, the solution to the equation ln(5 - 2^x) = 0 is x ≈ 2.