Solve for x: 2^(2x-3) imes 2^(x+2) = 128

April 28, 2026Mathematics

ScanSolve AI Answer

April 28, 2026

Answer

$\frac{8}{3}$

Step 1: Rewrite the equation. The given equation is $2^{(2x-3)} \times 2^{(x+2)} = 128$ .

Step 2: Apply the exponent rule $a^m \times a^n = a^{m+n}$ to the left side of the equation. $2^{(2x-3) + (x+2)} = 128$ Combine the exponents: $2^{(2x+x-3+2)} = 128$ $2^{(3x-1)} = 128$

Step 3: Express the right side of the equation as a power of 2. We know that $2^7 = 128$ . So, substitute this into the equation: $2^{(3x-1)} = 2^7$

Step 4: Equate the exponents since the bases are the same. $3x - 1 = 7$

Step 5: Solve the linear equation for $x$ . Add 1 to both sides: $3x = 7 + 1$ $3x = 8$ Divide by 3: $x = \frac{8}{3}$

The value of $x$ is $\boxed{\frac{8}{3}}$ .

That's 2 down. 3 left today — send the next one.

Was this helpful?

Need help with your own homework?

Get instant step-by-step solutions to any question. Free to start.

Ask Your Question

Handwritten Step-by-Step Solution

Get this as a handwritten image on WhatsApp — like a tutor wrote it for you.

Try on WhatsApp

More Mathematics Questions

QUsing a scale of 2cm to 1 unit on both axes, draw the graph of y=2x+5 for the values of x from -3 to…Q4x2 + 12x + 8 Qएक स्कूल के अनुपस्थित छात्रों की संख्या प्रतिदिन 147 दिनों तक दर्ज की गई थी तथा प्राप्त आँकड़े निम्न…QIf y = sinh(ksin⁻¹x), show that (1-x²)y'' - xy' - k²y = 0 Qनिम्नलिखित संचयी बारम्बारता बंंटन से विद्यार्थियों के अंकों का समान्तर माध्य ज्ञात कीजिए—

See all Mathematics questions →

Still have questions?

Quick Answer

Rewrite the equation. The given equation is 2^(2x-3) × 2^(x+2) = 128.

Asked on April 28, 2026Mathematics

This mathematics problem involves applying core mathematical principles and formulas. Below you will find a complete step-by-step solution with detailed explanations for each step, helping you understand not just the answer but the method behind it.

ScanSolve AI AnswerAnswered on April 28, 2026

Step 1: Rewrite the equation. The given equation is 2^(2x-3) × 2^(x+2) = 128. Step 2: Apply the exponent rule a^m × a^n = a^m+n to the left side of the equation. 2^(2x-3) + (x+2) = 128 Combine the exponents: 2^(2x+x-3+2) = 128 2^(3x-1) = 128 Step 3: Express the right side of the equation as a power of 2. We know that 2^7 = 128. So, substitute this into the equation: 2^(3x-1) = 2^7 Step 4: Equate the exponents since the bases are the same. 3x - 1 = 7 Step 5: Solve the linear equation for x. Add 1 to both sides: 3x = 7 + 1 3x = 8 Divide by 3: x = (8)/(3) The value of x is (8)/(3). That's 2 down. 3 left today — send the next one.