Solve for oc in the exponential equation 4²x-1 = 1/16

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The question asks to solve for x in the exponential equation 4^(2x−1) × 8^(x+3) = 16. Step 1: Express all bases as powers of 2. 4 = 2²; 8 = 2³; 16 = 2⁴ Step 2: Substitute these into the given equation. (2²)^(2x−1) × (2³)^(x+3) = 2⁴; Step 3: Apply the exponent rule (a^m)ⁿ = a^(mn) to simplify the terms on the left side. 2^(2(2x−1)) × 2^(3(x+3)) = 2⁴; 2^(4x−2) × 2^(3x+9) = 2⁴; Step 4: Apply the exponent rule a^m × aⁿ = a^(m+n) to combine the terms on the left side. 2^((4x−2) + (3x+9)) = 2⁴; 2^(4x−2+3x+9) = 2⁴; 2^(7x+7) = 2⁴ Step 5: Since the bases are equal, equate the exponents. 7x+7 = 4 Step 6: Solve the linear equation for x. 7x = 4 − 7; 7x = −3; x = −3/7 The value of x is −3/7.

Solve for oc in the exponential equation 4²x−1 = 1/16

Answer

Step-by-step solution

Express all bases as powers of 2.

Substitute these into the given equation.

Apply the exponent rule $(a^m)^n = a^{mn}$ to simplify the terms on the left side.

Apply the exponent rule $a^m \times a^n = a^{m+n}$ to combine the terms on the left side.

Since the bases are equal, equate the exponents.

Solve the linear equation for $x$ .

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