SOLUTION: solve each equation. If the answer is not exact give the answer to 4 decimal places. 3^(x+3)+3^x=84 4^(x+2)-4^x=15

Question 384403: solve each equation. If the answer is not exact give the answer to 4 decimal places.
3^(x+3)+3^x=84
4^(x+2)-4^x=15
Answer by jsmallt9(3758) (Show Source): You can put this solution on YOUR website!

One way to solve this involves factoring in a way you may not have seen/done before. The first term on the left is the product of x+3 3's. The second term is the product of x 3's. So both terms have x 3's in common. We can factor out those x 3's from each term. After we factor out the x 3's, the first term will still have 3 3's. The second term will just be a 1 since we factored out all of its 3's:

which simplifies to:

Dividing both sides by 28 we get:

So x = 1

This problem can be solved in a similar way:

And so, if you remember how zero exponents work, x = 0.
RELATED QUESTIONS
Solve the following equation. Give exact answer to and a decimal aproximation to 2... (answered by Alan3354)

is this true or false: 3log(b)√3:(a)=log[b](a) assume that x,y,z are positive... (answered by Edwin McCravy)

Solve the equation. Round your answer to two decimal places when appropriate. (X+4)^3... (answered by Alan3354)

Can anyone give me a hand with this one? Thanks Solve the equation. If answer is not (answered by josmiceli)

Please Help! Solve the equation and give the exact answer. Then if necessary, use a... (answered by lwsshak3)

6^(3-4x) x 4^(x+4) = 2 Solve giving answer to 2 decimal... (answered by MathLover1)

I am absolutely lost on these type of equations. Your assistance is deeply required.... (answered by Fombitz)

Determine the nature of the solutions of the equation 10t^2 - 8t = 0. 2) give exact and... (answered by ewatrrr)

Give exact and approximate solutions to 3 decimal places. (x+4)^2=36 Please help me (answered by solver91311)