Solve the equation $5^x = 17,$ giving your answer to 3 significant figures. - Edexcel - A-Level Maths Pure - Question 6 - 2007 - Paper 2

To solve the equation, we can use logarithms. Taking the logarithm of both sides, we have:

egin{align*} ext{log}(5^x) &= ext{log}(17) \\ x imes ext{log}(5) &= ext{log}(17) ext{, where log represents the logarithm to any base, commonly base 10 or natural log.} egin{align*}

Next, isolate $x$:

$$x = \frac{\text{log}(17)}{\text{log}(5)}$$

Now, we compute the values:

• Using a calculator, find:
  • $ext{log}(17) \approx 1.230449$
  • $ ext{log}(5) \approx 0.699

Substituting these values gives:

$$x \approx \frac{1.230449}{0.699} \approx 1.7595$$

Rounding this to three significant figures, we get:

$$x \approx 1.76$$