Question

if 5^x + 5^x-1 = 150, then the value of x is :

Answer 1

Try approximation techniques. Let f(x) = 5^(x+1) + 5x. You want f(x) = 150.First, try x = 2. Then f(2) = 5^3 + 10 = 135. Since this is too small, try x = 3. Here, you have f(3) = 5^4 + 15 = 640, which is much too large. This tells you the x you want is between 2 and 3, much closer to 2 than to 3.
Try then x = 2.1. Using a calculator, you find f(2.1) = 5^3.1 + 10.5 = 157.33.
So now x lies between 2 and 2.1, apparently closer to 2.1 than to 2. I swould now try x = 2.07, and continue in this manner until I obtained some f(x) very close to 150. Try it out!

Answer 2

Given:

$5^{x}+5^{x-1}=150$

To find:

The value of x.

Solution:

If $5^{x}+5^{x-1}=150, then the value of x is 3.$

We can solve the above mathematical problem using the following approach.

$5^{x}+5^{x-1}=150 can be written as-$

$5^{x}+\frac{5^{x}}{5^{1}}=150 (\because a^{-n} = \frac{1}{a^n})\\\\ 5^{x}\left(1+\frac{1}{5}\right)=150 \\\\ 5^{x}\left(\frac{6}{5}\right)=150 \\\\ 5^{x}=\frac{150 \times 5}{6} \\\\ 5^{x}=25 \times 5 \\\\ 5^{x}=5^{3} \\\\On comparing we get-\\\\x = 3.$

Therefore, the value of x is 3.