2log5-3log2+5log2
To simplify the expression 2log5 - 3log2 + 5log2, we can use the properties of logarithms:
1. log a + log b = log (ab)
2. log a - log b = log (a/b)
3. log a^b = b * log a
Using the properties above, we can rewrite the expression as:
2log5 - 3log2 + 5log2
= log5^2 - log2^3 + log2^5
= log25 - log8 + log32
= log(25/8) + log32
= log(25/8 * 32)
= log(200/8)
= log(25)
Therefore, 2log5 - 3log2 + 5log2 simplifies to log(25).
Log32+log128-log729/log32+log2-log27
To simplify the expression log32 + log128 - log729 / log32 + log2 - log27, we can use the properties of logarithms once again:
1. log a + log b = log (ab)
2. log a - log b = log (a/b)
3. log a^b = b * log a
Using these properties, we can rewrite the expression as:
log32 + log128 - log729 / log32 + log2 - log27
= log(32*128) - log729 / log32 + log2 - log27
= log4096 - log729 / log32 + log2 - log27
= log(4096/729) / log32 + log2 - log27
= log(56/9) / log32 + log2 - log27
= log(56/9) / (log2 + log16 - log27)
= log(56/9) / (log2 + 4log2 - 3log3)
= log(56/9) / (log2 + 4log2 - 3log3)
= log(56/9) / (log2 + 4(log2 - log3))
= log(56/9) / (log2 +4 log(2/3))
= log(56/9) / (log2 - log(3/2))+5
= log(56/9) / log(2/3))+5
= log(56/9) / (log2 - log3))+5
Now we have the expression in terms of logarithms, but it cannot be simplified further without knowing the values of log(56/9), log2, and log3.
Please note that log(56/9) = log(56) - log(9), log(2/3) = log(2) - log(3), and log(3/2) = log(3) - log(2).
To simplify the expression 2log5 - 3log2 + 5log2, you can use the properties of logarithms.
1. Start by combining the like terms:
2log5 - 3log2 + 5log2 = 2log5 + (5log2 - 3log2)
2. Simplify the expression inside the parentheses:
2log5 + (5log2 - 3log2) = 2log5 + 2log2
3. Use the logarithmic property that states log a + log b = log(ab) to combine the logarithms with the same base:
2log5 + 2log2 = log5^2 + log2^2
4. Apply the exponent property that states log a^n = n log a:
log5^2 + log2^2 = 2log5 + 2log2