How do you evaluate #log_(1/4) (1/16)#? Precalculus Properties of Logarithmic Functions Logarithm-- Inverse of an Exponential Function 1 Answer Alan P. Sep 20, 2016 #log_(1/4) (1/16)=color(green)(2)# Explanation: Remember: #color(white)("XXX")log_color(blue)(b) color(magenta)(a) =color(red)(c) hArr color(blue)(b)^color(red)(c)=color(magenta)(a)# Since #color(white)("XXX")color(blue)(""(1/4))^color(red)(2) = color(magenta)(1/16)# #rArr# #color(white)("XXX")log_(color(blue)(1/4)) color(magenta)(1/16) = color(red)(2)# Answer link Related questions What is a logarithm? What are common mistakes students make with logarithms? How can a logarithmic equation be solved by graphing? How can I calculate a logarithm without a calculator? How can logarithms be used to solve exponential equations? How do logarithmic functions work? What is the logarithm of a negative number? What is the logarithm of zero? How do I find the logarithm #log_(1/4) 1/64#? How do I find the logarithm #log_(2/3)(8/27)#? See all questions in Logarithm-- Inverse of an Exponential Function Impact of this question 4600 views around the world You can reuse this answer Creative Commons License