Solve for x: 3^{x}-3^{x-1}=486 | vedclass

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(B) Given equation: $3^{x}-3^{x-1}=486$We can rewrite $3^{x-1}$ as $\frac{3^{x}}{3}$:$3^{x}-\frac{3^{x}}{3}=486$Factor out $3^{x}$:$3^{x}(1-\frac{1}{3

Vedclass · Accepted Answer

$6$

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(B) Given equation: $3^{x}-3^{x-1}=486$We can rewrite $3^{x-1}$ as $\frac{3^{x}}{3}$:$3^{x}-\frac{3^{x}}{3}=486$Factor out $3^{x}$:$3^{x}(1-\frac{1}{3})=486$Simplify the expression inside the parentheses:$3^{x}(\frac{2}{3})=486$Multiply both sides by $\frac{3}{2}$:$3^{x}=486 	imes \frac{3}{2}$$3^{x}=243 	imes 3$$3^{x}=729$Express $729$ as a power of $3$:$729 = 3^{6}$Therefore,$3^{x}=3^{6}$,which implies $x=6$.

Solve for $x: 3^{x}-3^{x-1}=486$

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