The value of x in the given equation 4^x - 3^ | vedclass

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(B) Given equation: $4^x - 3^{x - 1/2} = 3^{x + 1/2} - 2^{2x - 1}$Rearranging the terms:$2^{2x} + 2^{2x - 1} = 3^{x + 1/2} + 3^{x - 1/2}$Factor out th

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$3/2$

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(B) Given equation: $4^x - 3^{x - 1/2} = 3^{x + 1/2} - 2^{2x - 1}$Rearranging the terms:$2^{2x} + 2^{2x - 1} = 3^{x + 1/2} + 3^{x - 1/2}$Factor out the common terms:$2^{2x - 1}(2 + 1) = 3^{x - 1/2}(3 + 1)$$2^{2x - 1}(3) = 3^{x - 1/2}(4)$Divide both sides by $3$ and $3^{x - 1/2}$:$\frac{2^{2x - 1}}{4} = \frac{3^{x - 1/2}}{3}$$2^{2x - 1 - 2} = 3^{x - 1/2 - 1}$$2^{2x - 3} = 3^{x - 3/2}$Rewrite the exponent on the left side:$2^{2(x - 3/2)} = 3^{x - 3/2}$$(2^2)^{x - 3/2} = 3^{x - 3/2}$$4^{x - 3/2} = 3^{x - 3/2}$Divide by $3^{x - 3/2}$:$\left(\frac{4}{3}\right)^{x - 3/2} = 1$Since $a^0 = 1$,we have:$x - 3/2 = 0$$x = 3/2$

The value of $x$ in the given equation $4^x - 3^{x - 1/2} = 3^{x + 1/2} - 2^{2x - 1}$ is

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