Question 492607: I need help with these questions
5^x=125
8^x+1=16^x
81^(3/4)=x
8^(-2/3)=x
log(base2)32=x
log(base x) (1/9)=-2
log(base4)x=3
Log(base3)(x+7)=Log(base3)(2x-1)
Answer by chessace(471)   (Show Source):
You can put this solution on YOUR website! Looks like you need more practice with exponents and logs.
1. [could just look at it and notice that 5^3 = 125].
Take lob(base 5) of both sides.
log(base 5)(5^x) = x by definition
log(base 5)(125) = 3 by the process of seeing how many 5's multiplied together it takes to reach 125.
2. 8^(x+1)=16^x = (8^2)^x = 8^(2x)
Base is same, exponents must be same: x+1=2x; x=1
3. x=81^(3/4)=(81^(1/4))^3 Note that 3^4 = 81, so
x = ((3^4)^1/4))^3 = (3^(4*(1/4)))^3 = (3^1)^3 = 3^3 = 27
4. note that 2^3 = 8. 8^(-2/3) = (2^3)^(-2/3) = 2^(-2) = -1/4.
5. x=log(base 2)32. How many 2's have to be mult together to get 32?
2 4 8 16 32: 5 of them. x=5.
6. statement implies that x^-2 = 1/9. x=3.
7. " " " 4^3 = x, x=64.
8. " " " x+7=2x-1. Solve for x.
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