which equation is equivalent to $\\log_{x}36 = 2$?\n$2^{x}=36$\n$x^{2}=36$\n$36^{x}=2$\n$x^{2}=36^{2}$
which equation is equivalent to $\\log_{x}36 = 2$?\n$2^{x}=36$\n$x^{2}=36$\n$36^{x}=2$\n$x^{2}=36^{2}$
Answer
Explanation:
Step1: Recall the logarithmic - exponential conversion formula
The formula for converting a logarithmic equation (\log_{a}b = c) to an exponential equation is (a^{c}=b), where (a) is the base ((a>0,a\neq1)), (b) is the argument ((b > 0)), and (c) is the logarithm value.
Step2: Identify the values of (a), (b), and (c) in the given logarithmic equation
In the equation (\log_{x}36 = 2), we have (a=x), (b = 36), and (c = 2).
Step3: Apply the conversion formula
Substituting (a=x), (b = 36), and (c = 2) into the formula (a^{c}=b), we get (x^{2}=36).
Answer:
(x^{2}=36) (the second option)