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Solve for x. {:[3^(10)=3^(7)*x^(3)],[x=◻]:}

Solve for x x .\newline310=37⋅x3x=□ \begin{array}{l} 3^{10}=3^{7} \cdot x^{3} \\ x=\square \end{array}

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Find higher derivatives of rational and radical functionsright chevron icon

Full solution

Q. Solve for x x .\newline310=37⋅x3x=□ \begin{array}{l} 3^{10}=3^{7} \cdot x^{3} \\ x=\square \end{array}
  1. Calculate Tape Rolls Needed: We need to divide the total amount of tape needed by the amount of tape on each roll. 8,000 cm÷2,000 cm/roll=4 rolls8,000 \, \text{cm} \div 2,000 \, \text{cm/roll} = 4 \, \text{rolls}
  2. Solve Exponential Equation: We have the equation 310=37×x33^{10} = 3^{7} \times x^{3}. To solve for xx, we can divide both sides by 373^{7}. 310÷37=x33^{10} \div 3^{7} = x^{3}
  3. Simplify Exponents: Now we simplify the left side by subtracting the exponents.\newline3(10−7)=x33^{(10-7)} = x^{3}\newline33=x33^{3} = x^{3}
  4. Find Value of x: Since 333^{3} is 2727, we have:\newline27=x327 = x^{3}
  5. Find Value of x: Since 333^{3} is 2727, we have:\newline27=x327 = x^{3} To find xx, we take the cube root of both sides.\newlinex=3x = 3

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