How do you inverse log in an equation using a scientific calculator?

Question

How would I get the log (lg) to the other side of this equation?

lg (d/10) = - 0.46

I want d/10 to be on one side, with the log and -0.46 on the other... How can I do this using my calculator?

Any help would be appreciated.

Answer 1

Raise it to the tenth power. d = 10^-04.6

Answer 2

First of all we need to determine what base log you are working in. Most scientific calculators work for log base 10 and log base 'e' only. These are normally indentified by lg and ln respectively (ln meaning the natural log).

So, let's assume by your equation above that you are working in log base 10.

You have to remember what the logarithm actually IS. The logarithm is the number raised to a power, so your equation:

log (d/10) = -0.46

is equivellent to

d/10 = 10^(-0.46)

Do you see how it works? The log function can't just be carried to the other side, because it represents the opposite to an exponential (not to be confused with the natural exponential, 'e' or 'exp')

On your calculator (probably as a second function on the log (lg) button) there will be a 10^x symbol. That is how you elliminate the log from the equation, it becomes:

d/10 = 10^(-0.46)

So if you need to find d:

d = 10 * 10^(-0.46) = 3.467

It is a simple as that.

PS: Stevers1 is on the right track, but his answer is wrong.

Answer 3

On a calculator use the 10^x button. On some calculators you have to do INV Log or 2nd Log etc. Basically you just need to do the opposite operation to the LOG key.

So for your problem, enter the following keys -

0
.
4
6
+/- (unary minus, sometimes shown as +/-, sometimes as (-) or just a small - sign)
10^x (or Inv LOG, or 2nd LOG depending on your calculator.)

Answer 4

with the help of inspection x+a million = -3 x = -4 I have been given the comparable answer, so I'sd think of your approach is right to put in the "steps" (2/3)^(x+a million) =27/8 .......... "notation revision" this is "widespread" log((2/3)^(x+a million)) =log(27/8) (x+a million)*log(2/3) = log(27/8) ... = log( 3^3 / 2^3) ... = log((3/2)^3) ... = 3*log(3/2) (x+a million)*log(2/3) = 3*log(3/2) (x+a million)*log(2/3) = 3*(-a million)*log(2/3) x+a million = -3 x = -4 /*************************/ notice: this step on your rationalization is incorrect ... could be a typo, despite if it is extremely incorrect: (2/3) x-a million = 27/8 <=========== no /***************/ (2/3) x-a million = 27/8 inverse , cancel out 2/3 to the two facet and on left will become unfavourable 27/8 = -9/4 that's x+a million = -3/a million --a million /***************/ i don't understand this area the type you clarify it.