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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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Please help!!
enot [183]

Since g(h(x))=h(g(x))= x, hence functions h and g are inverses of each other

Given the functions expressed as:

h(x) =\sqrt{2x+2}\\g(x)\frac{x^2-2}{2}  \\

In order to check whether they are inverses of each other, we need to show that h(g(x)) = g(h(x))

Get the composite function h(g(x))

h(g(x))=h(\frac{x^2-2}{2} )\\h(g(x))=\sqrt{2(\frac{x^2-2}{2} )+2}\\h(g(x))=\sqrt{x^2-2+2} \\h(g(x))=\sqrt{x^2}\\h(g(x))=x

Get the composite function g(h(x))

g(h(x))=\frac{(\sqrt{2x+2} )^2-2}{2} \\g(h(x))=\frac{2x+2-2}{2}\\g(h(x))=\frac{2x}{2}\\g(h(x))=x

Since g(h(x))=h(g(x))= x, hence functions h and g are inverses of each other

Learn more on inverse functions here; brainly.com/question/14391067

7 0
2 years ago
Read 2 more answers
Help meh pls
Iteru [2.4K]
Its 1+20x because you would subtract 2-1-=1 and 35x-15x=20x im sorry this is the real correct answer


4 0
3 years ago
Read 2 more answers
1 Solve for the unknown variable:
Burka [1]

Answer:

Approximately 6.4

Step-by-step explanation:

We can use the pythagorean thereom here, that tells us (a^2)+(b^2)=c^2. C is the hypotenuse, the side opposite from the right angle, while a and b are the other sides. We can insert 5 and 4 as a and b, and solve for c

:(5^2)+(4^2)=c^2

:25+16=c^2

:41=c^2

:sqrt(41)=6.4=c              (We square rooted both sides. 6.4 is only rounded to the nearest hundredths place.) Hope this helps!

8 0
2 years ago
Read 2 more answers
How to find x and also giving reason . Thanku
Colt1911 [192]
1a. x = 70 
     Alternate Interior Angles

1b. x = 120
     Alternate Interior Angles

1c. x = 110
     Corresponding Angles

2a. x = 100
      Alternate Interior Angles
      y = 80
      Supplementary Angles (with x)

2b. x = 75
      Corresponding Angles
      y = 105
      Supplementary Angles (with x)

2c. x = 70
      Same-Side Interior Angles 
      y = 110
      Supplementary Angles (with x)

Try the rest on your own! 


7 0
3 years ago
On Monday, three hundred ninety - two students went on a trip to the zoo. All nine buses were filled and five students had to tr
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The answer to your question is 43
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