Solve the following exponential equations: 274x = 9^x+1 and (1/8)⁻²x = 2^x+3.

Step 1: Solve 27^(4x) = 9^(x+1). We express both sides with the same base, 3. (3³)^(4x) = (3²)^(x+1); 3^(12x) = 3^(2(x+1)) Equate the exponents: 12x = 2x + 2; 10x = 2; x = 2/10; x = 1/5; The solution is x = 1/5. Step 2: Solve (1/8)^(−2x) = 2^(x+3). We express both sides with the same base, 2. (2⁻³)^(−2x) = 2^(x+3); 2^(6x) = 2^(x+3) Equate the exponents: 6x = x + 3; 5x = 3

Solve the following exponential equations: 274x = 9^x+1 and (1/8)⁻²x = 2^x+3.

Step 1: Solve 27^(4x) = 9^(x+1). We express both sides with the same base, 3. (3³)^(4x) = (3²)^(x+1); 3^(12x) = 3^(2(x+1)) Equate the exponents: 12x = 2x + 2; 10x = 2; x = 2/10; x = 1/5; The solution is x = 1/5. Step 2: Solve (1/8)^(−2x) = 2^(x+3). We express both sides with the same base, 2. (2⁻³)^(−2x) = 2^(x+3); 2^(6x) = 2^(x+3) Equate the exponents: 6x = x + 3; 5x = 3

Solved: Solve the following exponential equations: 274x…

Solve $27^{4x} = 9^{x+1}$ .
We express both sides with the same base, 3.
$(3^3)^{4x} = (3^2)^{x+1}$ $3^{12x} = 3^{2(x+1)}$
Equate the exponents:
$12x = 2x + 2$ $10x = 2$ $x = \frac{2}{10}$ $x = \frac{1}{5}$
The solution is $\boxed{x = \frac{1}{5}}$ .
Solve $(\frac{1}{8})^{-2x} = 2^{x+3}$ .
We express both sides with the same base, 2.
$(2^{-3})^{-2x} = 2^{x+3}$ $2^{6x} = 2^{x+3}$
Equate the exponents:
$6x = x + 3$ $5x = 3$

Solve the following exponential equations: 274x = 9^x+1 and ((1)/(8))⁻²x = 2^x+3.

Answer

Step-by-step solution

Solve $27^{4x} = 9^{x+1}$ .

Solve $(\frac{1}{8})^{-2x} = 2^{x+3}$ .

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