- Find the value of the unknown variable in each of these:
(i) 2^x = 128 , (ii) 3^y = 1/9 , (iii) 5^x = 625 , (iv) 4^s = 164 , (v) 16^t = 4 ,
(vi) 8^ = 1/4 . - Solve each of the following equations for the value of x (i) log 3x = 6
ii) log[3]x + 3log[3](3x) = 3 iii) log (5x - 1) = 2 + log (x - 2) iv) 2logx = log(7x - 12)
3. Write each of the following as a single logarithmic expression:
(i) log[10](x + 5) + 2 log[10] x (ii) log[4](x^3 - y^3) - log[4] (x - y)
iii) 1/2 (3 log[5] (4x) + log [5] (x + 3) - log[5] 9)
solution 1
ReplyDeletewhen finding the values of unknown as in these questions we first write:
2^3 = 8 <==> log[2] 8=3
i) 2^x = 128
log[2] 128 = x
so
log 128/log2 = x
7 = x
if we now put 7 as x we get 128 as the answer.
ii) 3^y = 1/9
log[3]1/9=y
log 1/9/log 3 = y
-2 = y
iii) 5^x = 625
log[5] 625 = x
log 625/log 5 = x
4 = x
iv) 4^s = 164
log[4] 164 = s
log 164/log 4 = s
3.68 = s
v) 16^t = 4
log[16] 4 = t
log 4/log 16 = t
0.5 = t
vi) 8^ = 1/4 .
i tink the variable x was supposed to be in this question so
8^x = 1/4
log[8] 1/4 = x
log1/4 / log8 = x
-0.67 = x