Final answer:
To solve the exponential equation 3ˣ/¹⁴=0.1, isolate the variable x by taking the natural logarithm of both sides. Then, solve for x by dividing, multiplying, and evaluating the expression.
Step-by-step explanation:
To find the solution of the exponential equation 3ˣ/¹⁴=0.1, we need to isolate the variable x. We can do this by taking the logarithm of both sides of the equation. In this case, we will use the natural logarithm (ln) to simplify the calculation.
Using the logarithmic property logb(a/b) = logb(a) - logb(b), we can rewrite the equation as:
x * ln(3) - (1/14) * ln(10) = ln(0.1)
Now, we can solve for x by dividing both sides of the equation by ln(3) and then multiplying by 14:
x = 14 * (ln(0.1) + (1/14) * ln(10)) / ln(3)
Using a calculator, we can evaluate this expression to find the solution to be approximately x = -1.8105, rounded to four decimal places.