evaluate these logarithms please...?

a ) log base 10
-----------------------
log 200 - log 100
log (200/100)
log 2

b ) log base 2
---------------------
log 4 + log 8
log 32
5

c ) Assume
log5 5 + log5 5 - log2 8
1 + 1 - 3
- 1

d)
(1/2) (6) + (1/3) (3)
3 + 1
4

=-2

c. log5 5 = log5 25 - log2 8
That will come out to 1 = -1
Did you type the problem correctly?

a)
log_10(200) - log_10(2)
= log_10(200/2)
= log_10(100)
= log_10(10^2)
= 2log_10(10)
= 2

b)
2log_2(2) + log_2(8)
= 2 + log_2(2^3)
= 2 + 3log_2(2)
= 2 + 3
= 5

c)
log_5(5) ≟ log_5(25) - log_2(8)
1 ≟ log_5(5^2) - log_2(2^3)
1 ≟ 2log_5(5) - 3log_2(2)
1 ≟ 2 - 3
1 ≠ -1
Therefore, log_5(5) = log_5(25) - log_2(8) is not true.

d)
1/2[log_2(64)] + 1/3[log_5(125)]
= 1/2[log_2(2^6)] + 1/3[log_5(5^3)]
= 1/2[6log_2(2)] + 1/3[3log_5(5)]
= 6/2 + 3/3
= 3 + 1
= 4

Remember that the log of a number to any base is the power to which the base must be raised to generate the number, e.g. log(10) 1000 = 3

a) log(100 200 - log(10) 2 = log(10) 200/2 = log(10) 100 = 2

b) 2 log(2) 2 + log(2) 8 = 2+3 = 5

c) log(5) 5 = log(5) 25 - log(2) 8 => 1=2-3. This is false, so I am guessing you missed the shift key when you typed it and you really meant:
c) log(5) 5 + log(5) 25 - log(2) 8 = 1 + 2 - 3 = 0

d) 1/2 log(2) 64 + 1/3 log(5) 125 = 3 + 1 = 4

a) log base 10 problem: log 200 = log 2 + log 100 So log 200 - log 2 = log 100 = 2 since 100 = 10^2.

b) log base 2 problem: log 2 = 1 since 2=2^1. log 8 = 3 since 8 = 2^3. So log 2 + log 8 = 1+3=4

c)bases 5 and 2 problem: 5=5^1, 25=5^2, 8=2^3 so the result is 1+2 - 3 = 0 assuming you meant to have a + instead of an = in the problem.

d) 64 = 2^6 and 125 = 5^3 so the answer is (1/2)*6 + (1/3)*3 = 3+1 = 4

(a)
formula is
log a-log b = log(a/b)
so ans is
log(200/2)
log 100
value of log 100 is 2
so ans is == 2
-----------------------------
thereis use of two formulas
log a+log b= log a*b
and
alogb = log b^a
so 2log2 2 +log2 8
= log 2 2^2 +log 2 8
= log2 4 +log2 8
= log 2 (4*8)
= log 2 32
= log 2 2^5
= 5

note formula is
loga a^b = b
---------------------------
(c)
=log5 25 - log2 8
= log5 5^2 - log 2 2^3
= 2- 3
=1
= log5 5
-----------------------
(d)
1/2 log2 64+1/3log 5 125
log2 64^1/2 +log5 125^1/3
log2 8 +log5 5
log 2 2^3 + log 5 5
3 +1
=4

a) log 200 - log 2 = log (200/2) = log 100 = 2

b) 2 log_2 2 + log_2 8 = log_2 4 + log_2 8 = log_2 32 = 5

c) log_5 5 + log_5 25 - log_2 8 = 1 + 2 - 3 = 0

d) (1/2) log_2 64 + (1/3) log_5 125 = (1/2) (6) + (1/3) (3) = 3 + 1 = 4

a)2
b)5
c)1≠ -1
d)4