Question

Consider the equation 14*10^0.5w=100

Answer 1

Step-by-step explanation:

14*10^0.5w=100

$14*10^{0.5w}=100$

Solve the equation for w

divide by 14 on both sides

$10^{0.5w}=\frac{100}{14}$

Convert exponential form into log form

base is 10 so we convert into log form

log (a)= x  then a=10^x

$10^{0.5w}=\frac{100}{14}$

$0.5w = log(\frac{100}{14} )\\0.5w = log(\frac{50}{7} )$

divide both sides by 0.5

$0.5w = log(\frac{50}{7} )\\\\\\w= 2 log(\frac{50}{7} )$

Answer:

$w= 2 log(\frac{50}{7} )$