What is the answer to 5(3^{2x-1})=243 ?

The answer to 5(3^{2x-1})=243 is x=(ln(729/5))/(2ln(3))

Solve for x: 5(3^{2x-1})=243

The solution is x=(ln(729/5))/(2ln(3))

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5 (3^{2 x - 1}) = 243

x = \frac{ln ( \frac{729}{5} )}{2 ln ( 3 )}

Decimal Notation

x = 2.26751 \dots

Solution steps

5 (3^{2 x - 1}) = 243

Divide both sides by

5

3^{2 x - 1} = \frac{243}{5}

Apply exponent rules

(2 x - 1) ln (3) = ln (\frac{243}{5})

Solve

(2 x - 1) ln (3) = ln (\frac{243}{5}) : x = \frac{ln ( \frac{729}{5} )}{2 ln ( 3 )}

x = \frac{ln ( \frac{729}{5} )}{2 ln ( 3 )}

3^{2 x} - 6 \cdot 3^{x + 1} - 243 = 0

\frac{( 2 x ^{7} )}{( 1 - x )} = 30

x, x^{2} + (y - \frac{4}{x ^{2}}) 2 = 1

\frac{1}{( 1 + x ^{a - b} )} + \frac{1}{( 1 + x ^{b - a} )} = 1

\frac{x ^{2} + 1}{( x ^{2} ) - 5 ( x + \frac{1}{x} ) + 8} = 0

What is the answer to 5(3^{2x-1})=243 ?
The answer to 5(3^{2x-1})=243 is x=(ln(729/5))/(2ln(3))
Solve for x: 5(3^{2x-1})=243
The solution is x=(ln(729/5))/(2ln(3))