logarithmic functions

[Guest]

How do you find these answers and how do you do them on the calculator?

1) log2(log3(x))=3

2) logb(9.34)=3

3) 8+5(2X)=79

4) 43X 42X-1=100

 

[stapel]

1) By definition, "log₂(log₃(x)) = 3" means "2³ = log₃(x)" or "8 = log₃(x)", which in turn means "x = 3⁸". Simplify.

2) This one works the same way.

3) This is just a linear equation. Solve by the usual methods.

4) I'm sorry, but I can't tell what this means. What do the subscripts indicate?

As for "how you do them on the calculator", that would probably depend on what you mean by "doing", and what calculator you have. Please reply with specifics. Thank you.

Eliz.

 

[Guest]

Thank you Eliz. In the #4 problem the smaller numbers in gray are the exponents.

 

[Guest]

Also, 3) 8+5(2X)=79 ---the "x" in 2x is supposed to be the exponent. Sorry about that.

 

[stapel]

Oh. So the equations are actually:

. . . . .3) 8 + 5(2^x) = 79

. . . . .4) (4^3x)(4^{2x - 1}) = 100

For (3), subtract "8" from both sides, divide through by 5, and take logs of both sides.

For (4), combine the two factors on the left-hand side by using exponent rules, and then take logs of both sides.

Eliz.