solve for x using logarithms round your answer to four decimal places.
a)2^2x+3=80
Suspect you mean
2^(2x+3) = 80
that means
(2x+3)log 2 = log 80
(2x+3) = 6.32192
2x = 3.32192
x = 1.6609
Ok,thanks!
You are welcome.
To solve the equation 2^(2x+3) = 80 using logarithms, follow these steps:
Step 1: Take the logarithm of both sides of the equation. The most commonly used logarithm is the natural logarithm (ln), denoted as log base e.
ln(2^(2x+3)) = ln(80)
Step 2: Use the logarithmic property that states log base a (a^b) = b * log base a (a) to simplify the equation:
(2x + 3) * ln(2) = ln(80)
Step 3: Divide both sides of the equation by ln(2) to isolate the term (2x + 3):
(2x + 3) = ln(80) / ln(2)
Step 4: Evaluate the right side of the equation using a calculator:
(2x + 3) ≈ 6.3219
Step 5: Subtract 3 from both sides of the equation:
2x ≈ 6.3219 - 3
2x ≈ 3.3219
Step 6: Divide both sides of the equation by 2:
x ≈ 3.3219 / 2
x ≈ 1.6609 (rounded to four decimal places)
Therefore, after rounding the answer to four decimal places, x is approximately 1.6609.