Solve the equation 14=65(19)x for x using logs.
To solve the equation 14 = 65(19)x using logs, we'll apply logarithms to both sides of the equation.
Step 1: Start by isolating the exponential term on one side of the equation. Divide both sides by 65(19) to get:
14 / (65(19)) = x
Step 2: Simplify the left side of the equation:
14 / (65(19)) = x
Step 3: Now, let's use logarithms to solve for x. In this case, we'll use the natural logarithm, denoted as ln:
ln(14 / (65(19))) = ln(x)
Step 4: Evaluate the left side of the equation using a calculator or math software:
ln(14 / (65(19))) ≈ -1.114
Step 5: Simplify the equation:
-1.114 = ln(x)
Step 6: Rewrite the equation in exponential form. The exponential form of ln(x) = -1.114 is:
x = e^(-1.114)
Step 7: Use a calculator or math software to evaluate e^(-1.114):
x ≈ 0.327
Therefore, the solution to the equation 14 = 65(19)x using logs is x ≈ 0.327.