http://tinypic.com/r/j8f6s0/6
^there's 2 parts to the problem, a and b.
please help with both if you can! and explain! I really don't understand..
^there's 2 parts to the problem, a and b.
please help with both if you can! and explain! I really don't understand..
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Alright so:
When you have to logs set equal to each other with the same base, you can basically just cross out the bases and set the exponents equal to each other.
For A:
First, make 16 in 4^2 so they have the same base.
4^2(x-1)=4^x+1
Then cancel out the 4s.
2(x-1)=x+1
Then distribute the 2.
2x-2=x+1
Subtract x and then add 2 to the other side and get x=3
For B:
When you are subtracting logs with the same base (the little number next to log,) you divide the number next to them (called an argument I think).
So: log(subscript 2) 6x/3=3
That simplifies to log(subscript 2)2x=3
Now, raise both sides to 2 to cancel out the log(subscript 2)
You get 2x=2^3
2x=8
x=4
When you have to logs set equal to each other with the same base, you can basically just cross out the bases and set the exponents equal to each other.
For A:
First, make 16 in 4^2 so they have the same base.
4^2(x-1)=4^x+1
Then cancel out the 4s.
2(x-1)=x+1
Then distribute the 2.
2x-2=x+1
Subtract x and then add 2 to the other side and get x=3
For B:
When you are subtracting logs with the same base (the little number next to log,) you divide the number next to them (called an argument I think).
So: log(subscript 2) 6x/3=3
That simplifies to log(subscript 2)2x=3
Now, raise both sides to 2 to cancel out the log(subscript 2)
You get 2x=2^3
2x=8
x=4