Describe and correct the error a student made when starting to solve the equation 8^x+3=2^2x-5 8^x+3=2^2x-5 (2^3)^x+3=2^2x-5 2^3x+3=2^2x-5 B. The student did not distribute 3in(2^3)^x+3 across x+3 C. The student should have expressed the initial rational exponent as the sum of two rational exponents. D. The student did not convert 8 to the correct power of 2 The correct answer is x=square (Simplify your answer.)

Question

Problemas

Describe and correct the error a student made when starting to solve the equation 8^x+3=2^2x-5 8^x+3=2^2x-5 (2^3)^x+3=2^2x-5 2^3x+3=2^2x-5 B. The student did not distribute 3in(2^3)^x+3 across x+3 C. The student should have expressed the initial rational exponent as the sum of two rational exponents. D. The student did not convert 8 to the correct power of 2 The correct answer is x=square (Simplify your answer.)

Answer 1

The student made an error in the second step of solving the equation. The correct way to rewrite $8^{x+3}$ is $(2^3)^{x+3}$, which simplifies to $2^{3(x+3)}$. Therefore, the correct equation should be $2^{3(x+3)}=2^{2x-5}$. From there, we can equate the exponents to get $3(x+3)=2x-5$. Solving this equation gives $x=-\frac{14}{5}$.<br /><br />The correct answer is $x=-\frac{14}{5}$.

Problemas

Solución

Responder