# Simplifying logarithmic expressions

1. Oct 18, 2009

### fatima_a

simplify the following expression

log2 4^3x-1 (2 is a subscript of log and 3x - 1 is a superscript of 4)

i can rearrange this to 4log2 3x - 1,
i am thinking after this it becomes 4 log3 + 4 logx, but i dont know what to do with the -1

please show all the steps and explain.
1. The problem statement, all variables and given/known data

2. Relevant equations

3. The attempt at a solution

2. Oct 18, 2009

### LCKurtz

You need to use parentheses to keep your variables straight. And use the Go Advanced button so you have access to the X2 and X2 superscript and subscript buttons. Using these buttons, you expression looks like this: log2 4(3x-1)

Write 4 as 22 and use the property of logs that says:

loga(ab) = b

and don't lose track of your parentheses.

3. Oct 19, 2009

### HallsofIvy

Staff Emeritus
You appear to be thinking that "$log(b^x)= b log(x)$". That is wrong. The correct formula is [itex]log(b^x)= x log(b)[itex].

No, "log (a+ b)" is NOT equal to "log(a)+ log(b)" but that is no longer relevant.

Go back and review the "laws of logarithms".