decimal form of
log_9 1,620
To find the decimal form of log base 9 of 1,620, you can use the change of base formula for logarithms:
log base b of x = log base c of x / log base c of b
In this case, we want to find log base 9 of 1,620, so we can use any base to compute the logarithm, as long as it's consistent. Let's choose base 10:
log base 9 of 1,620 = log base 10 of 1,620 / log base 10 of 9
Now, we can use a calculator to evaluate these logarithms:
log base 10 of 1,620 = 3.20951501438
log base 10 of 9 = 0.95424250943
Plugging in the values:
log base 9 of 1,620 = 3.20951501438 / 0.95424250943
Doing the division:
log base 9 of 1,620 ≈ 3.36533923549
Therefore, the decimal form of log base 9 of 1,620 is approximately 3.36533923549.
To find the decimal form of log base 9 of 1,620, you can use the logarithmic relation:
log_b(x) = y if and only if b^y = x.
In this case, we want to find y such that 9^y = 1,620. To solve for y, we can use trial and error by finding a value of y that satisfies the equation.
Let's begin:
9^1 = 9 (not equal to 1,620)
9^2 = 81 (not equal to 1,620)
9^3 = 729 (not equal to 1,620)
9^4 = 6,561 (not equal to 1,620)
9^5 = 59,049 (not equal to 1,620)
It seems that y = 5 is too large. Let's try a smaller value:
9^0 = 1 (equal to 1,620)
We found our answer: y = 0.
Therefore, log base 9 of 1,620 (log_9 1,620) is equal to 0 in decimal form.
To find the decimal form of log base 9 of 1,620, you can use the logarithmic identity:
log base b of x = log base c of x / log base c of b
In this case, we want to find log base 9 of 1,620, and we can use the common logarithm (log base 10) as the intermediary step. Therefore,
log base 9 of 1,620 = log base 10 of 1,620 / log base 10 of 9
To find the value of log base 10 of 1,620, you can use a calculator or a logarithm table. The log base 10 of 1,620 is approximately 3.209. Similarly, the log base 10 of 9 is approximately 0.954.
Now, substitute these values back into the equation:
log base 9 of 1,620 = 3.209 / 0.954
Calculating this expression, we get:
log base 9 of 1,620 ≈ 3.362
So, the decimal form of log base 9 of 1,620 is approximately 3.362.