Use the like-bases property and exponents to solve the equation

Ask by Rodriquez West. in the United States

Dec 07,2024

Question

Use the like-bases property and exponents to solve the equation $$ 10^{n+8}=10^{4 n-2} $$ $$ n=\square $$

UpStudy AI · Accepted Answer

Solve the equation $$ 10^{n+8}=10^{4n-2} $$.
Solve the equation by following steps:
- step0: Solve for $$n$$:
  $$10^{n+8}=10^{4n-2}$$
- step1: Set the exponents equal:
  $$n+8=4n-2$$
- step2: Move the variable to the left side:
  $$n+8-4n=-2$$
- step3: Subtract the terms:
  $$-3n+8=-2$$
- step4: Move the constant to the right side:
  $$-3n=-2-8$$
- step5: Subtract the numbers:
  $$-3n=-10$$
- step6: Change the signs:
  $$3n=10$$
- step7: Divide both sides:
  $$\frac{3n}{3}=\frac{10}{3}$$
- step8: Divide the numbers:
  $$n=\frac{10}{3}$$
The solution to the equation $$10^{n+8}=10^{4n-2}$$ is $$n=\frac{10}{3}$$ or $$n=3.\dot{3}$$.
$$ n=\frac{10}{3} $$ or $$ n=3.\dot{3} $$

Use the like-bases property and exponents to solve the equation

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