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3 years ago

Find a and b if2^a×3^b=12

Mathematics

1 answer:

krok68 [10]3 years ago

6 0

Answer:

12=12

Step-by-step explanation:

2a = b

a -3b =12

To solve, set one of the equations equal to zero. The first equation is actually already set to 0.

b = 2a

Now you can plug this equation into the other one, by substituting the b in the equation with this.

a -3b = 12

a – 3(2a) = 12

Now all you have to do is distribute the 3 (multiply the number outside the parenthesis, 3 in this case, by everything inside).

a – 6a = 12

Combine like terms. Since we have 1 positive a and 6 negative ones, we subtract the two numbers without the signs

6-1 = 5

And take the sign of the larger number. Since 6 is large and 6 is negative, we are left with

-5a = 12

Now solve for a, which in this case means dividing both sides by -5

a = -12/5

Simplify

a = -2.4

Now that you have a, it’s easy to find b

b = 2a

b = 2(-2.4)

b= -4.8

Now you check your work by plugging your new a and b into either equation to see if it’s true.

-4.8 = 2(-2.4)

-4.8 = -4.8

And just for laughs let’s try the other equation

a -3b =12

-2.4 – 3(-4.8) = 12

Distribute the 3 again. Remember that when two negative numbers are multiplied they become positive.

-2.4 +14.4 = 12

12 = 12

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A rational number can be expressed in the form of $\frac{p}{q}$ , where p and q are integers and q is not equal to 0. For example $2,3.5,\frac{2}{5},...$ .

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If any number is multiplied by a irrational number then the resultant number is an irrational number.

By the above definition we can conclude that:

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Therefore 0.01045 is a rational number.

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2 years ago

Find a and b if2^a×3^b=12​

Find a and b if2^a×3^b=12