What is the answer to 243sqrt(3)=3^x ?

The answer to 243sqrt(3)=3^x is x= 11/2

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243sqrt(3)=3^x

2433 = 3^{x}

x = \frac{11}{2}

Decimal Notation

x = 5.5

Solution steps

2433 = 3^{x}

Apply exponent rules

\frac{11}{2} = x

Switch sides

x = \frac{11}{2}

x e^{x} = \frac{1}{2}

\frac{3 6 ^{3 + 2 n}}{6 ^{n}} = 1

4^{6 x + 3} = 3 2^{x (5 - x)}

7^{2 x} - 11 (7^{x}) + 10 = 0

3 \cdot 4^{x} + 4^{x - 1} = 208