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
For this case we must solve the following equation:
[tex]8 + 5 ^ x = 1008[/tex]
Subtracting 8 on both sides of the equation:
[tex]5 ^ x = 1008-8\\5 ^ x = 1000[/tex]
We apply Neperian logarithm to both sides of the equation:
[tex]ln (5 ^ x) = ln (1000)[/tex]
We use the rules of the logarithms to draw x
of the exponent.
[tex]xln (5) = ln (1000)[/tex]
We divide both sides of the equation between[tex]ln (5)[/tex]:
[tex]x = \frac {ln (1000)} {ln (5)}\\x = 4.29202967[/tex]
Rounding:
[tex]x = 4.2920[/tex]
Answer:
[tex]x = 4.2920[/tex]
