subject of formula, how to solve, past exam questions

Question

1. Make y the subject of formula: t=(w/g)log(1+[y/Z) 2. Make y the subject of formula: q=3p[2-log(y/2)] 3. Make n the subject of formula: s=[ a(r^n -1)/ r-1 ] 4. Make P2 the subject of formula: H=100log(P1/P2)

Answer 1

1.

t = (w/g)log(1+[y/Z])

Multiply each side by g .

gt = g(w/g)log(1+[y/Z])

(w)log(1+[y/Z]) = gt

Divid each by w.

log(1+[y/Z]) = gt/w

Use basic principal of logarthims, log₁₀ (a) = x =>  a = 10^x

1+[y/Z] = 10^gt/w

y/Z = 10^gt/w - 1

y = Z (10^gt/w - 1)

Answer 2

2.

q=3p[2-log(y/2)]

Divide each side by 3p .

2-log(y/2) = q/3p

log(y/2)= 2 - q/3p

log(y/2)= (6p - q)/3p

Use basic principal of logarthims, log₁₀ (a) = x =>  a = 10^x

y/2= 10^{(6p - q)/3p}

y = 2(10^{(6p - q)/3p})

Answer 3

s=[ a(r^n -1)/ r-1 ]

Multiply each side by r -1 .

a(r^n -1) = s (r -1)

Divide each side by a .

r^n -1 = s (r -1)/a

Add 1 to each side

r^n =[s (r -1)/a] +1

Take logarithm both sides.

nlogr = log {[s (r -1)/a] +1}

n = log {[s (r -1)/a] +1}/logr

 

Answer 4

4)

H=100log(P1/P2)

Divide each side by 100.

log(P1/P2) = H/100

Use basic principal of logarthims, log₁₀ (a) = x =>  a = 10^x

(P1/P2) =10^H/100

P2 =P1/10^H/100