SOLUTION: Evaulate the logarithm: log7 343

Question 271169: Evaulate the logarithm:
log7 343
Answer by jsmallt9(3758) (Show Source): You can put this solution on YOUR website!

There are no calculators I know of which will calculate a base 7 logarithm. So to evaluate this logarithm we must

Evaluate it "by hand". This can be done if the argument is a known power of the base.
Convert the base to one your calculator "knows", base 10 or base e (ln).

Since you posted this question I'm guessing you didn't even try to find out if 343 was a power of 7:

Bingo! So = 3.

If you forget to check for a power of the base or if the argument is not a power of the base, then you must change the base of the logarithm to base 10 or base e (so we can use our calculators to find them). The formula for converting bases of logarithms is: . Using this to change the base 7 logarithm we get:

Both of these will work and they will both give the same answer. (See ** below.) Use your calculator on both if you don't believe me.

** When you use a calculator to find logarithms, you get decimal approximations most of the time. These decimal approximations are correct only up to the number of decimal places your calculator uses. (And the last decimal place will be a rounded-off digit.) So when you use your calculator for this problem you might not get exactly 3 because of the rounding and dropped-off digits. You might get 3.00000001 or 2.9999999 or something close to 3 instead of the exact, correct value of 3. And using log vs. ln may also result in a very, very small difference. (But both numbers will still be close to 3.)

Because of these approximations, it is good to find logarithms "by hand" if possible.

RELATED QUESTIONS
1. Find the logarithm log7(343) 2. solve 2log... (answered by ewatrrr)

log10 1000+ log7... (answered by LinnW)

I am trying to evaulate the expression of the logarithmic equation. Log(7) the square... (answered by ewatrrr)

Write the equation 7^3 = 343 in logarithmic form. a. log3 343 = 7 b. log7 343 = 3 c.... (answered by stanbon)

Log7 37/49 + log7 343 - log7 37/7 (answered by Fombitz,Alan3354)

simplify the following as single logarithm.... (answered by Alan3354)

Write the logarithmic expression as a single logarithm: log7 x+log7 y-log7 z. I got the... (answered by Alan3354,stanbon)

Expand each logarithm log7 22xyz (answered by richwmiller)

Condense the expression to a single logarithm with a leading coefficient of 1 using the... (answered by MathLover1)