Keywords:
logarithmic equation, variable, logarithm, logarithm properties
For this case we have a logarithmic equation in which we must find the value of the variable x. For this we must apply properties of logarithm. By definition we have:
[tex]log_ {b} (a) = c[/tex] is equivalent to [tex]b ^ c = a[/tex]
Applying the definition, we have that: [tex]log_ {5} (x + 30) = 3[/tex] must be equivalent to: [tex]5 ^ 3 = x + 30[/tex]
Solving the resulting equation we have:
[tex]125 = x + 30[/tex]
Clearing x:
[tex]x = 125-30\\x = 95[/tex]
Thus, the value of x is given by 95.
Answer:
The solution of[tex]log_ {5} (x + 30) = 3[/tex] is [tex]x = 95[/tex]
