A-Level Edexcel Maths Pure Geometric Sequences & Series: Find, to 3 significant figures,

Find, to 3 significant figures, the value of x for which 5^x = 7 - Edexcel - A-Level Maths Pure - Question 6 - 2008 - Paper 2

Question 6

Find, to 3 significant figures, the value of x for which 5^x = 7. Solve the equation 5^2 - 12(5^x) + 35 = 0.

Worked Solution & Example Answer:Find, to 3 significant figures, the value of x for which 5^x = 7 - Edexcel - A-Level Maths Pure - Question 6 - 2008 - Paper 2

Step 1

96%

114 rated

Answer

To solve for x in the equation $5^x = 7$ , we can take the logarithm of both sides. Using the logarithm properties, we have:

$x = \frac{\log 7}{\log 5}$

Calculating this gives:

$x \approx \frac{0.8451}{0.6990} \approx 1.21$

Thus, to three significant figures, the value of x is 1.21.

Step 2

99%

104 rated

Answer

To solve the equation $5^2 - 12(5^x) + 35 = 0$ , we can substitute $y = 5^x$ .

This transforms our equation into:

$y^2 - 12y + 35 = 0$

Next, we can factor this quadratic equation:

$(y - 5)(y - 7) = 0$

Thus, we have two potential solutions for y:

Since $y = 5^x$ , we substitute back:

For $y = 5$ , we have $5^x = 5$ which gives $x = 1$ .
For $y = 7$ , we have $5^x = 7$ , which will return to our previous equation to give $x \approx 1.21$ .

Therefore, the solutions for the equation are $x = 1$ and $x \approx 1.21$ .