# 2.1.3 Solve for x 2.2 Make Rs the subject of the formula? Relevance

2^(x + 2) + 2^(x) / 4 + 2^(x) + 42

(2^2) * (2^x) + (2^x) / 4 + (2^x) = 42

(4 + (1/4) + 1) * 2^(x) = 42

(5 + 1/4) * 2^(x) = 42

(21/4) * 2^(x) = 42

2^x = 42 * 4 / 21

2^x = 2 * 4

2^x = 8

x = 3

V = R / (R[s] + r) * V[dc]

V / (R * V[dc]) = 1 / (R[s] + r)

R * V[dc] / V = R[s] + r

R * V[dc] / V  -  r  =  R[s]

• A few mistakes in his answer. Then again, one needs to be respectful and have a keen eye to see the mistakes.

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• V = R / (R_s + r) * V_dc

We can multiply the numerators on the right side to simplify this:

V = RV_dc / (R_s + r)

Now multiply both sides by the denominator to get rid of the denominators:

V(R_s + r) = RV_dc

Distribute the left side:

R_sV + rV = RV_dc

Subtract rV from both sides:

R_sV = RV_dc - rV

Now divide both sides by V:

R_s = (RV_dc - rV) / V

We can simplify this to:

R_s = RV_dc/V - r

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• 2.2)  Multiply by (R_s + r) each side. Divide by V each side.  Subtract r each side.

What do you get? Done!

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