Math / Algebra

QuestionSolve the equation analytically. $2^{2 x-5}=16$
The solution set is $\square$ (Simplify your answer.)

Studdy Solution

STEP 1

1. The equation $2^{2x-5} = 16$ is exponential.
2. We will need to express both sides of the equation with the same base to solve for $x$ .

STEP 2

1. Express 16 as a power of 2.
2. Equate the exponents.
3. Solve for $x$ .

STEP 3

Express 16 as a power of 2. Since $16 = 2^4$ , we can rewrite the equation as:
$2^{2x-5} = 2^4$

STEP 4

Since the bases are the same, we can equate the exponents:
$2x - 5 = 4$

STEP 5

Solve for $x$ by isolating it. First, add 5 to both sides:
$2x - 5 = 4$ $2x = 4 + 5$ $2x = 9$
Next, divide both sides by 2:
$x = \frac{9}{2}$
The solution set is:
$\boxed{\frac{9}{2}}$

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QuestionSolve the equation analytically. $2^{2 x-5}=16$
The solution set is $\square$ (Simplify your answer.)

Studdy Solution

STEP 1

1. The equation $2^{2x-5} = 16$ is exponential.
2. We will need to express both sides of the equation with the same base to solve for $x$ .

STEP 2

1. Express 16 as a power of 2.
2. Equate the exponents.
3. Solve for $x$ .

STEP 3

Express 16 as a power of 2. Since $16 = 2^4$ , we can rewrite the equation as:
$2^{2x-5} = 2^4$

STEP 4

Since the bases are the same, we can equate the exponents:
$2x - 5 = 4$

STEP 5

Solve for $x$ by isolating it. First, add 5 to both sides:
$2x - 5 = 4$ $2x = 4 + 5$ $2x = 9$
Next, divide both sides by 2:
$x = \frac{9}{2}$
The solution set is:
$\boxed{\frac{9}{2}}$

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QuestionSolve the equation analytically. 22x−5=162^{2 x-5}=1622x−5=16The solution set is □\square□ (Simplify your answer.)

Studdy Solution

STEP 1

1. The equation 22x−5=16 2^{2x-5} = 16 22x−5=16 is exponential.2. We will need to express both sides of the equation with the same base to solve for x x x.

STEP 2

1. Express 16 as a power of 2.2. Equate the exponents.3. Solve for x x x.

STEP 3

Express 16 as a power of 2. Since 16=24 16 = 2^4 16=24, we can rewrite the equation as:22x−5=24 2^{2x-5} = 2^4 22x−5=24

STEP 4

Since the bases are the same, we can equate the exponents:2x−5=4 2x - 5 = 4 2x−5=4

STEP 5

Solve for x x x by isolating it. First, add 5 to both sides:2x−5=4 2x - 5 = 4 2x−5=4 2x=4+5 2x = 4 + 5 2x=4+5 2x=9 2x = 9 2x=9Next, divide both sides by 2:x=92 x = \frac{9}{2} x=29​ The solution set is:92 \boxed{\frac{9}{2}} 29​​

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QuestionSolve the equation analytically. $2^{2 x-5}=16$
The solution set is $\square$ (Simplify your answer.)

1. The equation $2^{2x-5} = 16$ is exponential.
2. We will need to express both sides of the equation with the same base to solve for $x$ .

1. Express 16 as a power of 2.
2. Equate the exponents.
3. Solve for $x$ .

Express 16 as a power of 2. Since $16 = 2^4$ , we can rewrite the equation as:
$2^{2x-5} = 2^4$

Since the bases are the same, we can equate the exponents:
$2x - 5 = 4$

Solve for $x$ by isolating it. First, add 5 to both sides:
$2x - 5 = 4$ $2x = 4 + 5$ $2x = 9$
Next, divide both sides by 2:
$x = \frac{9}{2}$
The solution set is:
$\boxed{\frac{9}{2}}$