Write each logarithmic expression as a single logarithm:
Log 2 + 3 log 1
2log5+log36-log9=log5*2 +log 36-log 9 =log25+log36-log9=log25+log36-log9=log25×36÷9=log10*2=2×1=2log10=2 the final answer is 2
To write the given logarithmic expression as a single logarithm, we can use the properties of logarithms.
1. Start with the given expression: log 2 + 3 log 1.
2. Recall that log 1 = 0, since any number raised to the power of 0 equals 1.
3. Substitute log 1 with 0: log 2 + 3(0).
4. Simplify the expression: log 2 + 0.
5. Since any number added to 0 remains the same, the expression simplifies to: log 2.
Therefore, the given logarithmic expression, log 2 + 3 log 1, can be written as a single logarithm as log 2.
To write each logarithmic expression as a single logarithm, we need to combine the given terms using the properties of logarithms. Let's start with the first expression:
Log 2 + 3 log 1
First, let's evaluate the second term, 3 log 1. The logarithm of 1 to any base is always 0, so we have:
3 log 1 = 3 * 0 = 0
Now, we can rewrite the expression as:
Log 2 + 0
Any number added to 0 is equal to itself, so:
Log 2 + 0 = Log 2
Therefore, the original expression Log 2 + 3 log 1 simplifies to Log 2 as a single logarithm.
log2+ 3log1
= log 2 + 3(0) = log2
you SHOULD know that log 1 = 0