Solve for the missing variable.
4^x =2
Example:
3^2n+1 = 3^4
Cross out both the threes
2n+1 =4
Subtract 1
2n=3
n=3/2
1. 4^x = 2.
Take Log of both sides:
x*Log4 = Log2,
X = Log2/Log4 = 0.5.
1. Or 4^x = 2.
(2^2)^x = 2^1,
2x = 1, X = 0.5.
To solve for the missing variable in an exponential equation, such as 4^x = 2, we can use logarithms.
Step 1: Take the logarithm of both sides of the equation. A common choice is the natural logarithm (ln), but any logarithm with a consistent base will work.
ln(4^x) = ln(2)
Step 2: Use the properties of logarithms to simplify the equation. The exponent rule states that ln(a^b) = b * ln(a).
x * ln(4) = ln(2)
Step 3: Divide both sides of the equation by ln(4) to isolate the variable x.
x = ln(2) / ln(4)
Step 4: Use a calculator to evaluate the right-hand side of the equation.
x ≈ 0.5
Therefore, the missing variable x is approximately equal to 0.5.