How do I solve exponential equations?

[ccvispartan]

We are currently studying logarithmic and one of the subsection is on solving exponential equations.

I cannot, for the life of me, solve this equation or similar equations. My hopes are that some of you guys can solve it for me and demonstrate the entire process.

The question is:

4^(x+1)+4^x=160

Correct answer of x is 2.5 but i do not know how to get there.

 

[D H]

Start by expressing 4^x+1 as 4*4^x and 4^x as 1*4^x. Now collect the common term on the left hand. Can you see the rest?

 

[ccvispartan]

Start by expressing 4^x+1 as 4*4^x and 4^x as 1*4^x. Now collect the common term on the left hand. Can you see the rest?

how do I actually collect like terms?

 

[D H]

how do I actually collect like terms?

Consider the expression a*b + a*c. Collect the common term. Now do the same to your problem.

 

[ccvispartan]

Start by expressing 4^x+1 as 4*4^x and 4^x as 1*4^x. Now collect the common term on the left hand. Can you see the rest?

Consider the expression a*b + a*c. Collect the common term. Now do the same to your problem.

5*4^x? if that's the term then the equation gives me an answer of 1.5 rather than 2.5

 

[D H]

No, it gives 2.5. Show your work.