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3 years ago

Solving exponential equations with a common base problem in the picture!

Mathematics

1 answer:

Genrish500 [490]3 years ago

7 0

<u>Given</u>:

The given expression is $18^{x^{2}+4 x+4}=18^{9 x+18}$

We need to determine the solution of the given expression.

<u>Solution</u>:

Let us solve the exponential equations with common base.

Applying the rule, if $a^{f(x)}=a^{g(x)}$ then $f(x)=g(x)$

Thus, we have;

$x^{2}+4 x+4=9 x+18$

Subtracting both sides of the equation by 9x, we get;

$x^{2}-5 x+4=18$

Subtracting both sides of the equation by 18, we have;

$x^{2}-5 x-14=0$

Factoring the equation, we get;

$x^2-7x+2x-14=0$

Grouping the terms, we have;

$(x^2-7x)+(2x-14)=0$

Taking out the common term from both the groups, we get;

$x(x-7)+2(x-7)=0$

Factoring out the common term (x - 7), we get;

$(x+2)(x-7)=0$

$x+2=0 \ and \ x-7=0$

$x=-2 \ and \ x=7$

Thus, the solution of the exponential equations is x = -2 and x = 7.

Hence, Option C is the correct answer.

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astraxan [27]

ANSWER

The value of the expression is
$- 1$

EXPLANATION

Method 1: Rewrite as product of
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The expression given to us is,

${i}^{0} \times {i}^{1} \times {i}^{2} \times {i}^{3} \times {i}^{4}$

We use the fact that
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to simplify the above expression.

${i}^{0} \times {i}^{1} \times {i}^{2} \times {i}^{3} \times {i}^{4} = {i}^{0} \times {i}^{1} \times {i}^{3} \times {i}^{2} \times {i}^{4}$

This implies,

${i}^{0} \times {i}^{1} \times {i}^{2} \times {i}^{3} \times {i}^{4} = {i}^{0} \times {i}^{2} \times {i}^{2} \times {i}^{2} \times {i}^{2} \times {i}^{2}$

We substitute to obtain,

${i}^{0} \times {i}^{1} \times {i}^{2} \times {i}^{3} \times {i}^{4} = 1\times - 1 \times - 1 \times - 1\times - 1 \times - 1$

${i}^{0} \times {i}^{1} \times {i}^{2} \times {i}^{3} \times {i}^{4} = 1\times 1 \times 1 \times - 1 = - 1$

Method 2: Use indices to solve.

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This implies that,

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Degger [83]

Answer:

Table shown below

Step-by-step explanation:

To solve this problem let's use proportions.

If 2 pounds of grapes cost $6, half the amount will cost half the dollars, so the last row will have $3 in the price

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2 years ago

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mariarad [96]

Comment
You have to begin by declaring what g(f(x)) means. It means that wherever you see an x in g(x) you put in f(x).

It will look like this to start with
g(f(x)) = (f(x) + 5) / (f(x)

Now substitute into this for g(-3)

g(x^2 + 5) = (x^2 + 5 + 5)/(x^2 + 5) It's time to use some numbers.
g(- 3) = ((-3)^2 + 10)/( (-3)^2 +5)
g(-3) = ( 9 + 10 ) / ( 9 + 5)
g(-3) = (19)/14 <<<<<< answer.
C <<<< answer.

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