exponential equations

[blackmage]

good day I have 2 problems that I can't for the life of me solve.

2^(x+3) + 2^x = 288

i know some how its suppose to become
2^x(2^3) + 2^x(1)=288
if someone can explain how to get this it would help me greatly


my other question is 3^(g+3) - 3^(g+2)= 1458

if you can help i would be eternally grateful

 

[galactus]

good day I have 2 problems that I can't for the life of me solve.

2^(x+3) + 2^x = 288

i know some how its suppose to become
2^x(2^3) + 2^x(1)=288
if someone can explain how to get this it would help me greatly

Let's rewrite it this way by using exponent laws:

\(\displaystyle 2^{x}\cdot 2^{3}+2^{x}=288\)

Factor:

\(\displaystyle 2^{x}(2^{3}+1)=288\)

Now, can you finish?.

my other question is 3^(g+3) - 3^(g+2)= 1458

Do the same as I done above:

\(\displaystyle 3^{g}\cdot 3^{3}-3^{g}\cdot 3^{2}=1458\)

Now, factor out 3^g and continue.

 

[pka]

good day I have 2 problems that I can't for the life of me solve.

2^(x+3) + 2^x = 288

That is same as \(\displaystyle 8\cdot 2^x+2^x=288\).
Or \(\displaystyle 9\cdot 2^x=288\).
Divide by 9.