Half-life solving for x

Question

40 = 50(.5)^(x/6537) solve for x

Answer 1

Given the equation solve for x

40 = 50(1/2)^(x/6537)

STEP 1) work towards the isolation of x by first moving 50 to the left side

4/5 = (1/2)^(x/6537)

STEP 2) work towards the isolation of x by applying ln to both sides

ln (4/5) = ln [ (1/2)^(x/6537) ]

STEP 3) work towards the isolation of x by applying log rules moving x/6537 from power position to coefficient position

ln (4/5) = ln [ (1/2) ] * (x/6537)

STEP 4) work towards the isolation of x by dividing ln(1/2) to the left side

ln (4/5) / ln(1/2) = (x/6537)

STEP 5) work towards the isolation of x by multiplying 6537 to the left side

x = [6537]*[ln (4/5) / ln(1/2)]

x is approx 2104.44395...

STEP 6) Check the answer

40 == 50(1/2)^( 2104.44395/6537)

true

thus x = 2104.44395