Question

6^x+6^(x+1)=2^x+2^(x+1)+2^(x+2)

Answer 1

6^x+6^(x+1)=6^x*(1+6)=7*6^x
2^x+2^(x+1)+2^(x+2)=2^x*(1+2+4)=7*2^x
7*6^x=7*2^x
(6/2)^x=1
3^x=1
x=0

Answer 2

6^х • ( 1 + 6 ) = 2^х • ( 1 + 2 + 4 )
6^х • 7 = 2^х • 7
6^х = 2^х
Х = 0

Answer 3

We can start by simplifying both sides of the equation using the properties of exponents:

6^x + 6^(x+1) = 2^x + 2^(x+1) + 2^(x+2)

6^x + 66^x = 2^x + 22^x + 42^x (since 6^(x+1) = 66^x and 2^(x+1) = 22^x and 2^(x+2) = 42^x)

Simplifying further, we get:

76^x = 72^x

Dividing both sides by 7, we get:

6^x = 2^x

Now we can solve for x by taking the logarithm of both sides with base 2:

log2(6^x) = log2(2^x)

xlog2(6) = xlog2(2)

x*(log2(6) - log2(2)) = 0

x*(log2(3)) = 0

Therefore, either x = 0 or log2(3) = 0. Since log2(3) is not equal to 0, the only solution is x = 0.

Therefore, the only solution to the equation 6^x + 6^(x+1) = 2^x + 2^(x+1) + 2^(x+2) is x = 0.