How to Solve Logarithmic Equations with Different Bases?

  • Thread starter Thread starter emma3001
  • Start date Start date
  • Tags Tags
    Logarithms
Click For Summary
To solve the equation log2x + log4x = 5, it's essential to clarify the interpretation of the logarithmic terms. If interpreted as log(2x) + log(4x) = 5, it simplifies to log(6x) = 5, making it straightforward to solve. However, if the intention is log2(x) + log4(x) = 5, converting log4(x) to a base of 2 is necessary, using the formula log_a(x) = log_b(x)/log_b(a). This conversion allows for solving the equation with a common base. Properly defining the logarithmic expressions is crucial for finding the correct solution.
emma3001
Messages
41
Reaction score
0
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.
 
Physics news on Phys.org
Convert them to the same base log_a(x)=log_b(x)/log_b(a).
 
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.
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.
log_4(x)= log_2(x)/log_2(4)= ?
 
Last edited by a moderator:
Dick said:
Convert them to the same base log_a(x)=log_b(x)/log_b(a).

can u help solving a problem?
 
can u help solve a problem?
 
Can u post the problem? Under Forum Tools, "Post a New Thread". That's your first step.
 

Thread 'Distance between a Clock's hands when the distance is increasing most rapidly'

Question: A clock's minute hand has length 4 and its hour hand has length 3. What is the distance between the tips at the moment when it is increasing most rapidly?(Putnam Exam Question) Answer: Making assumption that both the hands moves at constant angular velocities, the answer is ## \sqrt{7} .## But don't you think this assumption is somewhat doubtful and wrong?
View full post »

Similar threads

What is the solution to the complex cosine equation without using logarithms?
  • · Replies 7 ·
Replies
7
Views
2K
Logarithmic Regression Question (TI-84 Plus Graphing Calculator)
  • · Replies 4 ·
Replies
4
Views
2K
Efficient Logarithmic Calculations for 0.3048 without a Calculator
  • · Replies 8 ·
Replies
8
Views
2K
Prove this inequality using induction
  • · Replies 2 ·
Replies
2
Views
2K
Help with deriving relationships starting with the identity a^x = e^xlna
  • · Replies 5 ·
Replies
5
Views
2K
How Can I Solve a Differential Equation in Physics Homework?
  • · Replies 4 ·
Replies
4
Views
1K
Need Help Solving, Expanding, Rewriting, Graphing Logarithmic Functions
  • · Replies 5 ·
Replies
5
Views
2K
High School What Is the Physical Significance of Logarithmic IV Graphs in Diodes?
  • · Replies 3 ·
Replies
3
Views
5K
Derivative using Logarithmic Differentiation
  • · Replies 4 ·
Replies
4
Views
2K
Undergrad What is the logarithm of the derivative operator?
  • · Replies 10 ·
Replies
10
Views
2K