Solve for s: 11*12^s=396*2^s

Question

Help please

Answer 1

I'm assuming your asterisk equates to multiplication.  So your problem is...

11(12^s) = 396(2^s)

 

Let's get the variables on one side and the constants on the other

Divide each side by 2^s giving

 

11(12^s)/2^s = 396

 

Now divide both sides by 11

 

12^s/2^s = 396 /11

12^s/2^s = 36

 

Now we need to use logarithms to simplify this since logarithms are basically anti-exponents just as division is anti-multiplication.

 

log(12^s/2^s) = log36

 

Note:  log (a/b) = log a - log b    so

 

log 12^s - log 2^s = log 36

 

Note log aⁿ = n(log a)   so

 

s(log 12) - s(log 2) = log 36

 

Divide the "s" out of the two first terms giving

 

s(log 12 - log 2) = log 36

 

Now divide both sides by (log 12 - log 2) giving

 

s = log 36/(log 12 - log 2)

 

Now it's plug into the calculator and find the answer

 s = 2

 

Check:  11(12²) = 396(2²)

            11(144) = 396(4)

            1584 = 1584

            Thus we see that our answer is correct

 

 

Answer 2

11(12)^s = 396(12)^s

 

We want to solve for s.  We need to get all the terms with the exponent of s on one side of equation.

 

 

Divide both sides of equation by 11.

 

12^s = 36(2)^s

 

 

Divide both sides of equation by 2^s.

 

(12)^s / (2)^s = 36

 

 

According to the rules of exponents, we can divide the base numbers with a common exponent.

 

(12 / 2)^s = 36

 

6^s = 36

 

 

We know that if we raise 6 to the power of 2, we get 36.

 

s = 2