Exponential Equations (Grade 10 NSC Matric Mathematics): Quizzes

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Exponential Equations
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What is the defining feature of an exponential equation?

The unknown variable appears in the exponent

If ax=aya^x = a^y where a>0a > 0 and a≠1a \neq 1, what can you conclude?

x=yx = y

Why must a≠1a \neq 1 in the same base rule?

11 raised to any power always equals 11

Solve 3x+1=93^{x+1} = 9 using the same base method.

x=1x = 1

What is the solution to 3t=13^t = 1?

t=0t = 0

In 5t+3×5t+1=4005^t + 3 \times 5^{t+1} = 400, what should you factor out?

5t5^t

Why does 3x=−13^x = -1 have no real solution?

3x>03^x > 0 for all real xx

When should you consider substitution to create a quadratic?

When you see a2xa^{2x} and axa^x together

For a>0a > 0, what is true about axa^x for all real xx?

ax>0a^x > 0

In 2x−24−x=02^x - 2^{4-x} = 0, what technique eliminates the fraction?

Multiply both sides by 2x2^x

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