When solving: 3^x x 3^(x+1) x 3^x = 243

July 2, 2026Mathematics

ScanSolve AI Answer

July 2, 2026

Answer

Step 1: Combine the terms on the left side of the equation using the exponent rule $a^m \times a^n = a^{m+n}$ .

$3^x \times 3^{3x} \times 3^x = 243$ $3^{x + 3x + x} = 243$ $3^{5x} = 243$

Step 2: Express the right side of the equation, 243, as a power of 3.

$3^1 = 3$ $3^2 = 9$ $3^3 = 27$ $3^4 = 81$ $3^5 = 243$ So, we can rewrite the equation as: $3^{5x} = 3^5$

Step 3: Equate the exponents since the bases are the same.

$5x = 5$

Step 4: Solve for $x$ .

$x = \frac{5}{5}$ $x = 1$

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Quick Answer

Combine the terms on the left side of the equation using the exponent rule a^m × a^n = a^m+n.

Asked on July 2, 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 July 2, 2026

Step 1: Combine the terms on the left side of the equation using the exponent rule a^m × a^n = a^m+n. 3^x × 3^3x × 3^x = 243 3^x + 3x + x = 243 3^5x = 243 Step 2: Express the right side of the equation, 243, as a power of 3. 3^1 = 3 3^2 = 9 3^3 = 27 3^4 = 81 3^5 = 243 So, we can rewrite the equation as: 3^5x = 3^5 Step 3: Equate the exponents since the bases are the same. 5x = 5 Step 4: Solve for x. x = (5)/(5) x = 1 That's 2 down. 3 left today — send the next one.

Asked on July 2, 2026Mathematics

ScanSolve AI AnswerAnswered on July 2, 2026

Step 1: Combine the terms on the left side of the equation using the exponent rule a^m × a^n = a^m+n. 3^x × 3^3x × 3^x = 243 3^x + 3x + x = 243 3^5x = 243 Step 2: Express the right side of the equation, 243, as a power of 3. 3^1 = 3 3^2 = 9 3^3 = 27 3^4 = 81 3^5 = 243 So, we can rewrite the equation as: 3^5x = 3^5 Step 3: Equate the exponents since the bases are the same. 5x = 5 Step 4: Solve for x. x = (5)/(5) x = 1 That's 2 down. 3 left today — send the next one.