Solve for x

Question

2^x+1 - 2^x = 112

Put this in exponent form:
(3square root of x) ( square root of 3 cubed)

Put into equation form:
Horizontal stretch of 2, up 3, left 6, reflection on x-axis.

Please help me with these three so I can work on the rest using these as examples.

Thanks so much for your help!!!!:)

Answer 1

2^(x+1) - 2^x = 112
2(2^x) - 2^x = 112
2^x = 112
take log of both sides
log 2^x = log 112
x log2 = log112
x = log112/log2 = appr 6.81

check:
2^7.81 - 2^6.81 = 112.205... , not bad using only 2 decimals

(3square root of x) ( square root of 3 cubed)
( 3√x )( √(3^3)
= 3√x (√27)
= 3√x (3√3)
= 9√(3x)
or
9(3x)^(1/2)

your third question makes no sense

Answer 2

Mr.Reiny,

We don't use logs yet, so how do I find it without using log?

Answer 3

if you have not yet studied logs, this is a hard equation to solve.
The only other method I can think of is "trial and error" using your calculator

starting from 2^x = 112
you might look at powers of 2 to get an initial idea
after a few tries ...
2^6 = 64
2^7 = 128
so you know your answer is between 6 and 7, closer to 7
so try x = 6.5
2^6.5 = 90.5 , so go higher
try x = 6.75
2^6.75 = 107.6
getting closer, but go a little higher
try x = 6.8
2^6.8 = 111.43 , almost , how about ...
2^6.9 = 119.4 . ahhh , too high

can you follow what I'm doing?

Answer 4

Ill just use log then I think I get tht... but how did u come to 2^x=112...?

Answer 5

the original was
2^(x+1) - 2^x = 112

remember the rules for powers
we can write 2^(x+1) as (2^1)(2^x) , (just like 2^5 = 2(2^4) )

so we get
2(2^x) - 2^x = 112
2^x = 112 , (just like 2a -a = a)