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.
5. Find x, if:
(i) log3 x = 0
We have, log3 x = 0
So, 30 = x
1 = x
Hence, x = 1
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
Solve, using cross-multiplication:
8x + 5y = 9
3x + 2y = 4
Solve, using cross-multiplication:
√2x – √3y = 0
√5x + √2y = 0
2. The value of expression mx – ny is 3 when x = 5 and y = 6. And its value is 8 when x = 6 and y = 5. Find the values of m and n.
Given,
The value of expression mx – ny is 3 when x = 5 and y = 6.
? 5m – 6n = 3 … (i)
And,
The value of expression mx – ny is 8 when x = 6 and y = 5
? 6m – 5n = 8 … (ii)
Solving for m and n:
Performing (i)×6 – (ii)×5, we get
30m – 36n = 18
30m – 25n = 40
(-) (+) (-)
____________
-11n = -22
So,
n = 22/11
n = 2
Now, on substituting n = 2 in equation (i), we get
5m – 6(2) = 3
5m = 15
m = 3
? The solution is m = 3 and n = 2.
Find the value of m, if x = 2, y = 1 is a solution of the equation 2x + 3y = m.
Given, x = 2 and y = 1 is the solution of the equation 2x + 3y = m
Then,
2(2) + 3(1) = m
4 + 3 = m
? m = 7
Hence, if x = 2 and y = 1 is the solution of the equation 2x + 3y = m, then the value of m = 7.
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