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WINSTONCH [101]

3 years ago

9

Solve the linear equation:

title="4^{2x+7} = 8^{2x-3}" alt="4^{2x+7} = 8^{2x-3}" align="absmiddle" class="latex-formula">

1 answer:

g100num [7]3 years ago

8 0

Answer:

x = 11.5

Step-by-step explanation:

Taking the logarithm base 2 will transform this to a linear equation.

2(2x+7) = 3(2x -3)

0 = 3(2x -3) -2(2x +7) . . . . subtract the left side

0 = 2x -23 . . . . . . . . . . . . . simplify

0 = x - 23/2 . . . . . . . . . . . . divide by 2

11.5 = x . . . . . . . . . . . . . . . . add 11.5

The solution is x = 23/2 = 11.5.

_____

<em>Check</em>

This value of x makes the equation become ...

4^(2·23/2 +7) = 8^(2·23/2 -3)

4^30 = 8^20 . . . . . true

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Aleksandr-060686 [28]

$\LARGE{ \boxed{ \mathbb{ \color{purple}{SOLUTION:}}}}$

We have, Discriminant formula for finding roots:

$\large{ \boxed{ \rm{x = \frac{ - b \pm \: \sqrt{ {b}^{2} - 4ac} }{2a} }}}$

Here,

x is the root of the equation.
a is the coefficient of x^2
b is the coefficient of x
c is the constant term

1) Given,

3x^2 - 2x - 1

Finding the discriminant,

➝ D = b^2 - 4ac

➝ D = (-2)^2 - 4 × 3 × (-1)

➝ D = 4 - (-12)

➝ D = 4 + 12

➝ D = 16

2) Solving by using Bhaskar formula,

❒ p(x) = x^2 + 5x + 6 = 0

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$\large{ \rm{ \longrightarrow \: x = \dfrac{ - 5 \pm \sqrt{25 - 24} }{2 \times 1} }}$

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$\large{ \rm{ \longrightarrow \: x = \dfrac{ - 2 \pm \sqrt{ {2}^{2} - 4 \times 1 \times 1} }{2 \times 1} }}$

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So here,

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So here,

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kirza4 [7]

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