The discussion focuses on solving the logarithmic equation log2(x) + log4(x) = 5. Participants clarify the interpretation of the equation, emphasizing the need to convert logarithms to a common base for simplification. The conversion formula loga(x) = logb(x) / logb(a) is highlighted as a key technique. Ultimately, the equation can be simplified to log6(x) = 5, leading to an easier solution.
PREREQUISITESStudents, educators, and anyone looking to enhance their understanding of logarithmic equations and their applications in mathematics.
What do you mean by "log2x+ log4x= 5"? I would interpret that as log(2x)+ log(4x)= 5 so log(6x)= 5 which is easy. If you mean "log_2(x)+ log_4(x)= 5" then use Dick's hint.emma3001 said:Solve the equation log2x + log4x= 5. To start, should I change this to an exponential... I am stuck because I have only done log questions that have the same base.
Dick said:Convert them to the same base log_a(x)=log_b(x)/log_b(a).