Evaluate the expression, reducing to simplest form log(log1000^10000)=
BLANK +logBLANK
Your answers must be integers.
log 1000^10000 = 10000 log 1000
since 1000 = 10^3, log 1000 = 3
and you have
log(log1000^10000)
= log(10000*3)
= log 10000 + log3
= 4 + log3
To evaluate the expression log(log1000^10000), we can break it down into steps:
Step 1: Calculate the value of log1000^10000.
Since log1000^x = x, we have log1000^10000 = 10000.
Step 2: Calculate the logarithm of 10000.
The logarithm of 10000 in base 10 is 4, so log10000 = 4.
Step 3: Calculate the logarithm of 4.
The logarithm of 4 in base 10 is 0.602, so log4 = 0.602.
Therefore, the value of log(log1000^10000) reduces to 0 + log4.
To evaluate the expression log(log(1000^10000)), we'll simplify it step by step.
First, let's simplify the exponent 1000^10000. To do that, we raise 1000 to the power of 10000:
1000^10000 = 1 with 40003 zeros after it
Now, let's find the value of log(1 with 40003 zeros after it). The logarithm of any number raised to 1 is always 0:
log(1 with 40003 zeros after it) = 0
Finally, let's find the value of log(0). Logarithm of 0 is undefined, as there is no positive number that can be raised to any power to give 0.
Therefore, log(log(1000^10000)) cannot be evaluated as it leads to an undefined result.