SOLUTION: I would like help on these questions: log base 0.25 of sqrt2 - log base sqrt2 of 0.25 inverse of y=3*4^(x-1) + 2 thank you

Question 823335: I would like help on these questions:
log base 0.25 of sqrt2 - log base sqrt2 of 0.25
inverse of y=3*4^(x-1) + 2
thank you
Answer by jsmallt9(3758) (Show Source): You can put this solution on YOUR website!

The key to the first problem is to recognize that 0.25 and sqrt(2) are both powers of 2:

So by using the change of base formula to change these two logs into expressions of base 2 logs, we will get something that should simplify easily. The change of base formula:

Using this on both logs we get:

Since we already know what powers of 2 produce 0.25 and sqrt(2), we can replace all the logs:

Now we simplify:

Multiplying:

which simplifies as follows:

or 3.75
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