Question

Log12.8-log0.8+log(log625)

Answer 1

Ответ:

4

Пошаговое объяснение:

$log_{10} ( \frac{12.8 \times 625}{0.8} )$

$log_{10} (16 \times 625)$

$log_{10}(10000)$

$log_{10}(10 {}^{4} )$

Упростим выражение:

$log_{ \alpha }( \alpha ^{x} ) = x$

Answer 2

To simplify the expression, let's calculate each logarithm separately and then perform the arithmetic operations.

1. log12.8: Using the logarithmic identity log(a) + log(b) = log(a * b), we can rewrite log12.8 as log(12.8). log(12.8) is approximately equal to 1.1072.

2. log0.8: Similarly, log0.8 can be rewritten as log(0.8). log(0.8) is approximately equal to -0.0969.

3. log(log625): To calculate log(log625), we first find the value of log625 and then take its logarithm. log625 is the logarithm of 625 to the base 10, which is 2 because 10^2 = 100. log(2) is approximately equal to 0.3010.

Now let's substitute these values back into the expression and perform the arithmetic:

log12.8 - log0.8 + log(log625) = 1.1072 - (-0.0969) + 0.3010 = 1.1072 + 0.0969 + 0.3010 = 1.5051

Therefore, the value of the expression log12.8 - log0.8 + log(log625) is approximately 1.5051.