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:
\(log_ {b} (a) = c\) is equivalent to \(b ^ c = a\)
Applying the definition, we have that: \(log_ {5} (x + 30) = 3\) must be equivalent to: \(5 ^ 3 = x + 30\)
Solving the resulting equation we have:
\(125 = x + 30\)
Clearing x:
\(x = 125-30\\x = 95\)
Thus, the value of x is given by 95.
Answer:
The solution of\(log_ {5} (x + 30) = 3\) is \(x = 95\)
