Question

Q4 Q14.) Solve the following exponential equation by expressing each side as a power of the same base and then equating exponents.

Answer 1

Hello there!

Let me try this one out!

$6 ^{x-6} = \frac{1}{1296}$

We can start by taking log of both sides

$log(6 ^{x-6}) = log( \frac{1}{1296})$

$(x - 6)(log(6)) = log( \frac{1}{1296})$

Since we are solving for x:

$x - 6 = \frac{log(1/1296)}{log(6)}$

I used a calculator to help me solve the right part :)

x - 6 = - 4

Now we can add 6 on both sides

x - 6 + 6 = - 4 + 6

x = 2

I hope this helps! Let me know if you have any questions about the answer.