Solve each of the following equations for x. a) ln(5x)=0 x=? b) log_5 (2x)+log_5 (4x)=2 x=?

Rigoberto Drake 2022-11-19 Answered
Solve each of the following equations for x.
a) ln ( 5 x ) = 0 x = ?
b) log 5 ( 2 x ) + log 5 ( 4 x ) = 2 x = ?
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Answers (2)

Nigerkamg5
Answered 2022-11-20 Author has 20 answers
Suppose q = x 2 + 2 x is rational.
Then, by the quadratic formula, x = 2 ± 4 + 4 q 2 = 1 ± α , where α = q + 1 can be any rational number that is not a perfect square (since x is irrational).
Now,
x 3 6 x = ( 1 ± α ) 3 6 ( 1 ± α ) = ± α 3 / 2 3 α 3 α + 5
will be rational if and only if α 3 / 2 3 α is (since the other terms are always rational). But this is equal to α ( α 3 ). Since α 3 is rational and α irrational, the entire quantity will be rational iff it is zero: that is, iff α = 3.
Thus the numbers x that satisfy the condition are 1 ± 3
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Uroskopieulm
Answered 2022-11-21 Author has 4 answers
b) log 5 ( 2 x ) + log 5 ( 4 x ) = 2 log 5 ( 2 x ) ( 4 x ) = 2  take antilog on both sides  8 x 2 = 5 2 8 x 2 = 25 x 2 = 25 8 x = 25 8 x = 5 2 2 x = 5 2 4 x = 5 2 4 1.7678
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