Solve for x
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!!!!:)
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
Mr.Reiny,
We don't use logs yet, so how do I find it without using log?
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?
Ill just use log then I think I get tht... but how did u come to 2^x=112...?
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)
To solve the equation 2^(x+1) - 2^x = 112, we can manipulate the equation to isolate the variable x.
Step 1: Simplify the left side of the equation using exponent properties.
2^(x+1) - 2^x = 2^x * 2^1 - 2^x = 2 * 2^x - 2^x = 2^x
Step 2: Substitute 2^x back into the equation.
2^x = 112
Step 3: Take the logarithm of both sides of the equation using the base 2 logarithm, which is often written as log2.
log2(2^x) = log2(112)
x * log2(2) = log2(112)
Step 4: Simplify the equation further.
x = log2(112)
Using a calculator or logarithm table, you can find the approximate value of log2(112) to solve for x.
As for the second part of your question, to convert (3√x) (√3^3) to exponent form, we can rewrite the expression as:
(3√x) * (√3^3) = (x^(1/3)) * (3^(1/2))^3 = (x^(1/3)) * 3^(3/2)
Now, moving on to the third part, the information given about a horizontal stretch of 2, up 3, left 6, and reflection on the x-axis represents a sequence of transformations applied to a function.
A horizontal stretch of 2 means that the graph of the function is compressed by a factor of 2 horizontally.
An upward shift of 3 means the graph is shifted 3 units vertically.
A left shift of 6 means the graph is shifted 6 units to the right.
A reflection on the x-axis means that every point on the graph is reflected across the x-axis.
These transformations can be applied to the equation of a function to obtain the transformed equation. However, since you only provided a set of transformations and not the original equation, it is not possible to provide the specific equation as an example in this case.