Evaluate log2 raise to power 4 + log 4 raise to power 2-log 25 raise to power 5
To evaluate the expression log2^4 + log4^2 - log25^5, let's break it down step by step.
Step 1: Simplify the logarithmic expressions.
Using the logarithmic properties, we can rewrite each term:
log2^4 = 4 * log2
log4^2 = 2 * log4
log25^5 = 5 * log25
Step 2: Evaluate each logarithmic term.
Now we need to determine the value of each logarithmic expression.
First, calculate log2:
log2 is the exponent to which we raise the base (2) to get a certain number. In this case, we need to find 2 raised to the power of what gives us 2. So, log2(2) = 1.
Therefore, log2^4 becomes: 4 * log2 = 4 * 1 = 4.
Next, calculate log4:
Similar to the previous step, log4 is the exponent to which we raise the base (4) to get a certain number. In this case, we need to find 4 raised to the power of what gives us 4. So, log4(4) = 1.
Therefore, log4^2 becomes: 2 * log4 = 2 * 1 = 2.
Lastly, calculate log25:
Log25 is the exponent to which we raise the base (25) to get a certain number. In this case, we need to find 25 raised to the power of what gives us 25. So, log25(25) = 1.
Therefore, log25^5 becomes: 5 * log25 = 5 * 1 = 5.
Step 3: Combine the simplified expressions.
Now, we substitute our results back into the original expression:
4 + 2 - 5
Step 4: Compute the final result.
Finally, calculate the expression:
4 + 2 - 5 = 1
Therefore, log2^4 + log4^2 - log25^5 equals 1.
Is this the final answer
Is this the final answer
log2 raise to power 4 + log 4 raise to power 2-log 25 raise to power 5
why not just say:
log (2^4) + log (4^2) - log (25^5) ?
= log (2^4 * 4^2 / 25^5)
= log(16*16/9765625) = appr -4.58 ????
not sure if that is what you meant.