How Do You Solve Exponential Equations Using Logarithms?

AI Thread Summary
To solve the exponential equation 12^x = 4 * 8^(2x), logarithms are utilized. Taking the logarithm of both sides allows for simplification using the properties of logarithms, such as log(a*b) = log(a) + log(b) and log(a^b) = b*log(a). The discussion emphasizes the importance of applying these logarithmic rules to break down the equation. Participants encourage clarity in the steps rather than assuming prior knowledge of logarithmic concepts. Ultimately, the solution hinges on correctly applying logarithmic properties to simplify and solve for x.
moe11
Messages
8
Reaction score
0

Homework Statement


12^x=4X8^(2x)

Big X= multiplication sign
little x= unknown

i simply cannot figure this out. Any help please?

Homework Equations


4.6X1.06^(2x+3)=5X3^(x)
 
Physics news on Phys.org


Use logarithms! Isn't that your title? Take the log of both sides and use the rules of logarithms to simplify. What do you get?
 


Dick said:
Use logarithms! Isn't that your title? Take the log of both sides and use the rules of logarithms to simplify. What do you get?

i wouldn't post this if i could do it as easily as you said. Can you explain? Thats why I'm here.
 


log(12^x)=log(4*8^(2x)). That wasn't so hard. Now simplify it. Use rules of logarithms like, log(a*b)=log(a)+log(b), log(a^b)=b*log(a).
 


Your equation is 12x=(4)82x.

Since you titled this "logarithms", Dick assumed you knew some basic rules of logarithms. Take the logarithm of both sides: log(12x= log((4)82x)

Now use the fact that log(ab)= log(a)+ log(b) and that log(ax)= x log(a).
 

Thread 'Finding the number of ways to arrange identical balls in a circle (3 different colors)'

I tried to combine those 2 formulas but it didn't work. I tried using another case where there are 2 red balls and 2 blue balls only so when combining the formula I got ##\frac{(4-1)!}{2!2!}=\frac{3}{2}## which does not make sense. Is there any formula to calculate cyclic permutation of identical objects or I have to do it by listing all the possibilities? Thanks
View full post »

Thread 'Making the denominator of a certain fraction real'

Essentially I just have this problem that I'm stuck on, on a sheet about complex numbers: Show that, for ##|r|<1,## $$1+r\cos(x)+r^2\cos(2x)+r^3\cos(3x)...=\frac{1-r\cos(x)}{1-2r\cos(x)+r^2}$$ My first thought was to express it as a geometric series, where the real part of the sum of the series would be the series you see above: $$1+re^{ix}+r^2e^{2ix}+r^3e^{3ix}...$$ The sum of this series is just: $$\frac{(re^{ix})^n-1}{re^{ix} - 1}$$ I'm having some trouble trying to figure out what to...
View full post »

Similar threads

Solving a nested logarithmic equation
Replies
2
Views
2K
What Steps Are Missing to Solve (2x+5)^(x+1)=729?
Replies
11
Views
3K
Can this system of inequalities be solved for x?
Replies
5
Views
1K
Can you help me to find the solution of logarithm equation
Replies
6
Views
1K
Exponential and logarithmic Equation Problems
Replies
12
Views
2K
Solving for time in an exponential equation
Replies
12
Views
2K
How Do You Solve Exponential Inequalities Using Logarithms?
Replies
1
Views
2K
How Do You Set Up an Equation for the Ages of John, Peter, and Alice?
Replies
29
Views
2K
Can Logarithmic Properties Simplify This Equation?
Replies
12
Views
3K
How to Predict Outcomes of New Equations Without Solving for Variables?
Replies
18
Views
3K

Hot Threads

Recent Insights

Back
Top