Question

Consider the equation 14*10^0.5w=100

Solve the equation for w. Express the solution as a logarithm in base-10

Answer 1

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)=(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)=(100)/(14)`

`0.5w = log((100)/(14) )\\0.5w = log((50)/(7) )\\\\`

divide both sides by 0.5

`0.5w = log((50)/(7) )\\\\\\w= 2 log((50)/(7) )`

Answer:

`w= 2 log((50)/(7) )`