Exponential Equations With Different Bases

[nycmathguy]

The video is not too clear. How is this done?

 

[MathLover1]

2^x=5^(x+2)

log(2^x)=log(5^(x+2))

x*log(2)=(x+2)log(5)

x*log(2)=x*log(5)+2log(5)

x*log(2)-x*log(5)=2log(5)

x(log(2)-log(5))=2log(5)

x=2log(5)/(log(2)-log(5)) -> exact solution

 

[nycmathguy]

2^x=5^(x+2)

log(2^x)=log(5^(x+2))

x*log(2)=(x+2)log(5)

x*log(2)=x*log(5)+2log(5)

x*log(2)-x*log(5)=2log(5)

x(log(2)-log(5))=2log(5)

x=2log(5)/(log(2)-log(5)) -> exact solution

The exact answer must have the log, right?

 

[MathLover1]

right

 

[nycmathguy]

right

Copy. We will continue with College Algebra. We are currently in Chapter 1 and about to start Section 4 aka Polynomials. Going to work in 15 minutes. I may find time to post a few problems later if the building is not too crowded. Later....

P. S. No more probability until a future time. Probability is very humbling.