Question

Solve for x : 2^x+4^x+8^x=−14

Answer 1

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            Hi my lil bunny!

❧⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯☙

Let's solve this step by step.

$2^x + 4^x + 8^x = -14$

              ↓

In order to factor an integer, we need to repeatedly divide it by the ascending sequence of primes (2, 3, 5...).

The number of times that each prime divides the original integer becomes its exponent in the final result.

    Prime number 2 to the power of 2 = 4                

$2^x + (2^2)^x + (2^3) ^x = -14$

                    ↓

Prime number 2 to the power of 3 = 8

$2^x + 2^2x + 2^3x = -14$

                    ↓

We need to exponentiate the power.

The following rule is applied:

           $(A^B) ^C = A^BC$

In our example,

   A is equal to 2,

   B is equal to 2 and

   C is equal to x.

$( 2^x + 2^2x + 2^3x ) + 14 = -14 + 14$

                         ↑

In order to solve this non-linear equation, we need to move all the terms to the left side.

In our example,

- term −14, will be moved to the left side.

Notice that a term changes sign when it 'moves' from one side of the equation to the other.

___________________

We need to get rid of expression parentheses.

If there is a negative sign in front of it, each term within the expression changes sign.

Otherwise, the expression remains unchanged.

In our example, there are no negative expressions.

                                  ↓

            $2^x + 2^2x + 2^3x + 14 = 0$

❧⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯☙

●✴︎✴︎✴︎✴︎✴︎✴︎✴︎✴︎❀✴︎✴︎✴︎✴︎✴︎✴︎✴︎✴︎✴︎●

Hope this helped you.

Could you maybe give brainliest..?

❀*May*❀