Question

Solve 8 + 5^x = 1008. Round to the nearest ten-thousandth.

Answer 1

Answer: 4.29203

Explanation:

5^x=1008-8

5^x=1000

take the log of both sides

x=3 log 5 (10)

x=3+3log5(2)

or 4.29203

Answer 2

For this case we must solve the following equation:

`8 + 5 ^ x = 1008`

Subtracting 8 on both sides of the equation:

`5 ^ x = 1008-8\\5 ^ x = 1000`

We apply Neperian logarithm to both sides of the equation:

`ln (5 ^ x) = ln (1000)`

We use the rules of the logarithms to draw x

of the exponent.

`xln (5) = ln (1000)`

We divide both sides of the equation between
`ln (5)`:

`x = \frac {ln (1000)} {ln (5)}\\x = 4.29202967`

Rounding:

`x = 4.2920`

Answer:

`x = 4.2920`