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

Step 1: Combine the terms on the left side of the equation using the exponent rule a^m × aⁿ = 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. 3¹ = 3; 3² = 9; 3³ = 27; 3⁴ = 81; 3⁵ = 243 So, we can rewrite the equation as: 3^(5x) = 3⁵ Step 3: Equate the exponents since the bases are the same. 5x = 5 Step 4: Solve for x. x = 5/5; x = 1

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

Step 1: Combine the terms on the left side of the equation using the exponent rule a^m × aⁿ = 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. 3¹ = 3; 3² = 9; 3³ = 27; 3⁴ = 81; 3⁵ = 243 So, we can rewrite the equation as: 3^(5x) = 3⁵ Step 3: Equate the exponents since the bases are the same. 5x = 5 Step 4: Solve for x. x = 5/5; x = 1

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

July 2, 2026Mathematics

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Step-by-step solution

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Combine the terms on the left side of the equation using the exponent rule $a^m \times a^n = a^{m+n}$ .
$3^x \times 3^{3x} \times 3^x = 243$ $3^{x + 3x + x} = 243$ $3^{5x} = 243$
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:
$3^{5x} = 3^5$
Equate the exponents since the bases are the same.
$5x = 5$
Solve for $x$ .
$x = \frac{5}{5}$ $x = \boxed{1}$

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

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Step-by-step solution

Combine the terms on the left side of the equation using the exponent rule am×an=am+na^m \times a^n = a^{m+n}am×an=am+n.

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

Equate the exponents since the bases are the same.

Solve for xxx.

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

Solve for $x$ .