How to find
(7.27)^x=86.8
x log 7.27 = log 86.8 = 10 log 8.68
x log 7.27 = log 86.8
= log (10* 8.68) = log 10 + log 8.68
= 1 + log 8.68
To find the value of x in the equation (7.27)^x = 86.8, we need to use logarithms.
1. Start by taking the logarithm of both sides of the equation. The most commonly used logarithm is the natural logarithm (ln), so we'll use that here.
ln[(7.27)^x] = ln(86.8)
2. According to the logarithmic rule, ln(a^b) = b * ln(a), we can rewrite the left side of the equation:
x * ln(7.27) = ln(86.8)
3. Calculate ln(7.27) and ln(86.8) using a calculator or a computational tool. Let's assume ln(7.27) ≈ 1.986 and ln(86.8) ≈ 4.463.
x * 1.986 = 4.463
4. Divide both sides of the equation by 1.986 to isolate x.
x = 4.463 / 1.986
5. Calculate the result to find the value of x:
x ≈ 2.245
Therefore, x is approximately 2.245 in the equation (7.27)^x = 86.8.