Answer:
The required value of x in the given logarithmic equation is -0.36
Step-by-step explanation:
The given logarithmic equation is :
[tex]5^{2x}=\frac{5}{16}[/tex]
We need to find the required value of x in the given logarithmic equation.
[tex]5^{2x}=\frac{5}{16}\\\\\text{Taking log on both the sides}\\\\\log 5^{2x}=\log(\frac{5}{16})\\\\\implies 2x=\frac{\log 5-\log 16}{\log 5}\\\\\implies 2x=\frac{0.699-1.204}{0.699}\\\\\implies 2x = \frac{-0.505}{0.699}\\\\\implies 2x = -0.72\\\\\implies x = -0.36[/tex]
Hence, the value of x in the given logarithmic equation is -0.36
