Final answer:
To solve the equation for w, divide both sides by 14 to isolate the exponential term, then take the logarithm of both sides. Simplify using the properties of logarithms, and finally solve for w by dividing by the coefficient of w. The solution is w = 2log(7.142857).
Step-by-step explanation:
To solve the equation 14 • 10^{0.5w} = 100 for w, we first divide both sides by 14:
10^{0.5w} = \frac{100}{14}
10^{0.5w} = 7.142857
Now, to express w as a logarithm in base-10, we take the common logarithm of both sides:
\log(10^{0.5w}) = \log(7.142857)
By the property of logarithms, \log(10^a) = a, we can simplify the left-hand side to:
0.5w = \log(7.142857)
To find w, we divide both sides by 0.5:
w = \frac{\log(7.142857)}{0.5}
w = 2\log(7.142857)