Asked by Sam

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Log base 10^x=4

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Answered by Steve
your notation is bogus.

log base 10 (x) = 4
x = 10^4 = 10000

If that's not what you wanted, then 'splain what you mean. As written, you haven't specified a base. Just that you want the log of 10^x.

Take a look at other posted problems involving logs to see how to write it so we understand what you mean.
Answered by Sam
log10^x=4

the 10 is under the log
Answered by Steve
In that case, it's what I wrote above. Ditch the ^; it doesn't mean anything

assuming base 10,
log x = 4

means that 4 is the power of 10 needed to get x. 10^4 = 10,000 so log x = 4

Using base 3, log81 = 4 because 3^4 = 81

Log and ^ are inverse operations.

square root and square are inverses:
√x=5 means x = 5^2

multiplication and division are inverses:

x/3 = 5 means x = 3*5

addition/subtraction are inverses:

x-3 = 10 means x = 10+3

so, don't be stumped by logs; they're just powers written on the other side of the equation

log<sub>2</sub> (3x-1) = 8
means 3x-1 = 2^8

hang in there. I almost flunked my first test on logs. The book kept saying " a logarithm is an exponent" and I thought, "What? Just look at it -- it's nothing like an exponent!" Then a few days later it all clicked.
Answered by Sam
Okay thank you for the explanation!! Logarithms are difficult and get some use to.
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