Solve algebraically. Round to the nearest thousandth.
ln(5−2^x)=0
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.