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Solve for x : 4*3^(5x-5)=72

Solve for x x :\newline4⋅35x−5=72 4 \cdot 3^{5 x-5}=72

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Full solution

Q. Solve for x x :\newline4⋅35x−5=72 4 \cdot 3^{5 x-5}=72
  1. Simplify Equation: Simplify the equation by dividing both sides by 44.4⋅3(5x−5)=724\cdot3^{(5x-5)} = 723(5x−5)=7243^{(5x-5)} = \frac{72}{4}3(5x−5)=183^{(5x-5)} = 18
  2. Express as Power of 33: Express 1818 as a power of 33 to simplify the equation.\newline1818 can be written as 323^2.\newline35x−5=323^{5x-5} = 3^2
  3. Set Exponents Equal: Since the bases are the same, set the exponents equal to each other. 5x−5=25x - 5 = 2
  4. Solve for x: Solve for x by isolating x.\newline5x−5=25x - 5 = 2\newline5x=2+55x = 2 + 5\newline5x=75x = 7\newlinex=75x = \frac{7}{5}

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