Question

Find the exact solution to the equation. (5 points)
7-log_2(x+5) = 6
x = 3
x = 7
x = -3
x = -6

Answer 1

does that say log base 2?

Answer 2

yes

Answer 3

so the answer is 7?

Answer 4

@sweetburger

Answer 5

7-log_2(x+5) = 6

As before, subtract 7 from both sides,

OR,

alternatively,
Subtract 6 from both sides, obtaining \[1-\log_{2} (x-5)=0\]

Answer 6

Move the log term to the right side:\[1=\log_{2} (x-5)\]... How would you now solve for x-5, and then for x alone? Note that you must use 2 as base here, and the corresponding exponential function must also have base 2.

Answer 7

I have no idea...

Answer 8

Are you working on a test, a quiz or homework?
What have you done with logarithmic functions in the near past? exponential functions?

Answer 9

homework? And I am fairly new to this

Answer 10

Can you say how y=log x and y=10^x are related?

Answer 11

log is based by the number 10

Answer 12

Those two functions have the same base, yes. One is the inverse of the other. What does "inverse function" mean to you?

Answer 13

inverse means opposite

Answer 14

In this context "inverse" has a particular meaning.

if the log function is used as the INPUT to the base 10 expo. function, we must obtain the following:

\[10^{\log x}=x\]

Answer 15

Also, because these two are inverse functions,
\[\log 10^x=x\]

Answer 16

If you look carefully and think about this, you'll see that one of these functions "undoes" the other.

If I start with x and take the log to the base 10 of that, and then use the result as the exponent of 10, the result will be x, the quantity from which I started.

Answer 17

how does this relate to the problem

Answer 18

Given\[1=\log_{2} (x-5)\]

Answer 19

We want to find (1) x-5, and (2) x.
What is the base of this log system, and how do you know that?

Answer 20

This is a direct application of what we were discussing just before now.

Answer 21

base is x I believe

Answer 22

No, the base is 2. Earlier I used 10 as the base.

The same property applies here:\[2^{\log_{2}x }=x\] because these inverse functions "undo" each other.

Answer 23

Given \[1=\log_{2} (x-5)\]

Answer 24

how would you solve for x-5?

Answer 25

Recall: here the base is 2.

Answer 26

?? can you do it cause I am not understanding

Answer 27

Write '2' on both sides of a new equation.

Then use '1' as the exponent of the '2' on the left. Can you show me your work?

Answer 28

I cant not able to

Answer 29

Naveen, I have already led you through some examples. Have y ou not studied log functions and exponential functions before?

Answer 30

Im just confused and tired. 5 am where I live