Question

Find consecutive integers that are under and over estimates of the solutions to the following exponential equations.

10^x = 432,901

Answer 1

5 and 6

Explanation:

We have to first solve the given equation
`10^(x) =432901`

Now, taking log in the both sides we get,

`log10^(x) = log 432901`

⇒ x log 10=log 432901 {Since we have the logarithm property, log aᵇ =b log a}

⇒ x =log 432901 {Since log 10=1}

⇒ x=5.636.

Therefore, the consecutive integers that are under and over the value of x are 5 and 6. (Answer)