Divide the sum of
the sum of 5/8 and -11/8=-7/24
the difference of 3/7 and 5/14=-1/14
now divide the answers-7/24 by -1/14
-7/24 x 14/-1= 49/12
By what number should
the required number is 16 divided by -8/13
=16 x -13/8 = -26
write the method to synthesis of phenol?
2. Given log2 x = m and log5 y = n
(i) Express 2m-3 in terms of x
Given, log2 x = m and log5 y = n
So,
2m = x and 5n = y
(i) Taking, 2m = x
2m/23 = x/23
2m-3 = x/8
1. If loga m = n, express an – 1 in terms in terms of a and m.
We have, loga m = n
So,
an = m
Dividing by a on both sides, we get
an/a = m/a
an-1 = m/a
5. Find x, if:
(i) log3 x = 0
We have, log3 x = 0
So, 30 = x
1 = x
Hence, x = 1
We have,
log10 x = -2
10-2 = x [As loga c = b ? ab = c]
x = 10-2
x = 1/102
x = 1/100
Hence, x = 0.01
2. Express the following in exponential form:
(i) log8 0.125 = -1
We know that,
loga c = b ? ab = c
(i) log8 0.125 = -1
8-1 = 0.125
1. Express the following in logarithmic form:
10-3 = 0.001
10-3 = 0.001
log10 0.001 = -3
Solve, using cross-multiplication:
8x + 5y = 9
3x + 2y = 4
Given equations are 8x + 5y = 9 and 3x + 2y = 4
On comparing with a1x + b1y + c1 = 0 and a2x + b2y + c2 = 0, we have
a1 = 8, b1 = 5, c1 = -9 and a2 = 3, b2 = 2, c2 = -4
Now, x = (b1c2 – b2c1)/(a1b2 – a2b1) and y = (c1a2 – c2a1)/(a1b2 – a2b1)
x = [5 × (-4) – 2 × (-9)]/[8 × 2 – 3 × 5] and y = [ -9 × 3 – (-4) × 8]/[8 × 2 – 3 × 5]
x = (-20 + 18)/(16 – 15) and y = (-27 + 32)/(16 – 15)
x = -2/1 and y = 5/1
Therefore, x = -2 and y = 5
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