Solve for x. 8^7 = 8^3 * 8^x x = __

Identify base and exponents: Identify the base and the exponents in the equation 8^7 = 8^3 * 8^x. In this equation, 8 is the common base, and we have exponents 7, 3, and x.Apply property of exponents: Apply the property of exponents that states when multiplying like bases, you add the exponents. According to this rule: 8^a * 8^b = 8^(a+b). So, 8^3 * 8^x = 8^(3+x).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. 8^7 = 8^(3+x). Therefore, 7 = 3 + x.Solve for x: Solve for x by subtracting 3 from both sides of the equation. 7 - 3 = 3 + x - 3. This simplifies to: 4 = x.

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Solve for x. $8^7 = 8^3 \cdot 8^x$ x = __

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Math Problems

Grade 8

Solve equations with variable exponents

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Q. Solve for x.

8^7 = 8^3 \cdot 8^x

x = __

Identify base and exponents: Identify the base and the exponents in the equation $8^7 = 8^3 \times 8^x$ . In this equation, $8$ is the common base, and we have exponents $7$ , $3$ , and $x$ .
Apply property of exponents: Apply the property of exponents that states when multiplying like bases, you add the exponents. $\newline$ According to this rule: $\newline$ $8^a \times 8^b = 8^{(a+b)}$ . $\newline$ So, $8^3 \times 8^x = 8^{(3+x)}$ .
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. $\newline$ $8^7 = 8^{3+x}$ . $\newline$ Therefore, $7 = 3 + x$ .
Solve for x: Solve for x by subtracting $3$ from both sides of the equation. $\newline$ $7 - 3 = 3 + x - 3$ . $\newline$ This simplifies to: $\newline$ $4 = x$ .