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Solve for x. 87=83⋅8x8^7 = 8^3 \cdot 8^x x = __

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Full solution

Q. Solve for x. 87=83⋅8x8^7 = 8^3 \cdot 8^x x = __
  1. Identify base and exponents: Identify the base and the exponents in the equation 87=83×8x8^7 = 8^3 \times 8^x. In this equation, 88 is the common base, and we have exponents 77, 33, and xx.
  2. Apply property of exponents: Apply the property of exponents that states when multiplying like bases, you add the exponents.\newlineAccording to this rule:\newline8a×8b=8(a+b)8^a \times 8^b = 8^{(a+b)}.\newlineSo, 83×8x=8(3+x)8^3 \times 8^x = 8^{(3+x)}.
  3. Set exponents equal: Set the exponents of like bases equal to each other since the bases are the same on both sides of the equation.\newline87=83+x8^7 = 8^{3+x}.\newlineTherefore, 7=3+x7 = 3 + x.
  4. Solve for x: Solve for x by subtracting 33 from both sides of the equation.\newline7−3=3+x−37 - 3 = 3 + x - 3.\newlineThis simplifies to:\newline4=x4 = x.

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