What is the answer to 5^{x-3}*3^{2x}-8=225 ?

The answer to 5^{x-3}*3^{2x}-8=225 is x=(ln(233)+3ln(5))/(ln(45))

Solve for x: 5^{x-3}*3^{2x}-8=225

The solution is x=(ln(233)+3ln(5))/(ln(45))

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5^{x - 3} \cdot 3^{2 x} - 8 = 225

x = \frac{ln ( 233 ) + 3 ln ( 5 )}{ln ( 45 )}

Decimal Notation

x = 2.70035 \dots

Solution steps

5^{x - 3} \cdot 3^{2 x} - 8 = 225

Apply exponent rules

(lo g_{3} (5) (x - 3) + 2 x) ln (3) = ln (233)

Solve

(lo g_{3} (5) (x - 3) + 2 x) ln (3) = ln (233) : x = \frac{ln ( 233 ) + 3 ln ( 5 )}{ln ( 45 )}

x = \frac{ln ( 233 ) + 3 ln ( 5 )}{ln ( 45 )}

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

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

What is the answer to 5^{x-3}*3^{2x}-8=225 ?
The answer to 5^{x-3}*3^{2x}-8=225 is x=(ln(233)+3ln(5))/(ln(45))
Solve for x: 5^{x-3}*3^{2x}-8=225
The solution is x=(ln(233)+3ln(5))/(ln(45))