If 2ˣ = 4ˣ⁻¹, find x.
2
Given \(2^x = 4^{x-1}\).
Rewrite 4 as a power of 2: \(4^{x-1} = (2^2)^{x-1} = 2^{2(x-1)} = 2^{2x-2}\).
So the equation becomes \(2^x = 2^{2x-2}\).
Since the bases are equal, the exponents must be equal: \(x = 2x - 2\).
Solving, \(2x - x = 2 \Rightarrow x = 2\).
Similar Questions
If 27(x/3) = 9, find x.
Simplify the following expression:
\[ \left(\frac{x^2}{x^m}\right)^{1+m} \left(\frac{x^m}{x^n}\right)^{m+n} \left(\frac{x^n}{x^l}\right)^{n+l} \]
What is the cube root of 1728?
Evaluate √(19 - 6√10) + 3
Important Questions from Surds and Indices
Find the cube root of 78402752
What is the least number which, when multiplied by 28, forms a perfect square?
Find the value of :
[(3 × 3 × 3 × 3 × 3 × 3) 6 ÷ (3 × 3 × 3 × 3) 7 × 3 4]
The cube root of - 64 × - 1331 is:
If (27) m = (81) n, then m 2: mn = ?
