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Ann [662]
3 years ago
13

How to solve equations in which the variable is in an exponent

Mathematics
1 answer:
Temka [501]3 years ago
3 0

Answer:

It depends on the equation.

If the bases are equal and the variables are only in the exponents, set the exponents equal.

If there are variables in the exponents, but you cannot set the bases equal, then use logarithms.

Example 1:

4^{2x + 5} = 4^9

Here you have the same base on both sides. The variables are in the exponents. Set the exponents equal and solve for x.

2x + 5 = 9

2x = 4

x = 2

Example 2:

3^{2x} = 9^{6}

The bases are different, but you can make the bases equal using laws of exponents. Remember that 9 = 3^2.

3^{2x} = (3^2)^{6}

3^{2x} = 3^{12}

Now you have equal bases, so the exponents must be equal.

2x = 12

x = 6

Example 3:

10^{x + 2} = 9

Here you can't make the bases equal, so you take the log of both sides and use laws of logs.

\log(10^{x + 2}) = \log 3^2

(x + 2) \log 10 = 2 \log 3

Recall that: \log 10 = 1

x + 2 = 2 \log 3

x = 2 \log 3 - 2

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Step-by-step explanation:

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Bob and mark talk about their families. Bob says he has 3 kids, the product of their ages is 72. He gives another clue: the sum
pychu [463]
I can only give possible combination of the ages. Had the sum of the ages been given, then the 3 specific numbers would have been derived.

We need to do prime factorization of 72.

72 ÷ 2 = 36
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1 x 4 x 18 = 72         1 + 4 + 18 = 23
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3 0
3 years ago
Wright the ratio 4.5 : 2.35 in the form n : 1
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Answer:

\frac{9}{47}: 1

Step-by-step explanation:

you can divide both sides by 2.35 to get the right side to be 1:

4.5: 2.35\\\frac{9}{47}: 1

6 0
2 years ago
Which equation is rewritten in vertex form?
Zinaida [17]
(x + 3)^2 + (x + 4)^2 
= x^2 + 6x + 9 + x^2 + 8x + 16
= 2x^2 + 14x + 25
= 2(x^2 + 7x) + 25
= 2[(x + 7/2)^2  - 49/4] + 25
= 2(x + 7/2)^2 - 98/4 + 25
= 2(x + 7/2)^2 + 1/2


Its B

7 0
3 years ago
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