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Monday, December 30, 2013

Solving Logarithmic Equation, 3

Category: Algebra, Trigonometry

"Published in Newark, California, USA"

Solve for x:


Solution:

Consider the given equation above


Did you notice that the bases of the logarithmic functions are different? Well, we have to convert all the logarithmic functions into the same base first. Let's convert all the logarithmic functions into base 2 as follows

for


for


for


Hence, the given equation becomes






Take out their common factor, we have



Since the terms inside the bracket are all coefficients, then we can eliminate the coefficient since the right side of the equation is zero.



Take inverse logarithm on both sides of the equation




Take inverse tangent on both sides of the equation




Therefore, the answer is


I would like to thank Mr. Bilomba Nkita Leonard, Educator of Mathematics and Physical Sciences at Northwest Department of Education in South Africa who posted this problem at LinkedIn.