Question

logx² - log 2x = 3 log³ - Log⁶find the value of x​

Answer 1

Answer:

• The value of x is 9.

Step-by-step explanation:

Given that,

• logx² - log 2x = 3 log³ - Log⁶

↪ logx² - log 2x = 3 log³ - Log⁶ (x > 0)

Case (I),

[ °.° log a^{m} = m log a ]

↪ log x² = 2 log x _______eqn. (1)

Case (II),

[ °.° log (ab) = log (a) + log (b) ]

↪ log 2x = log 2 - log x _____eqn. (2)

From eqn. (1) & (2),

↪ 2 log x - log 2 - log x = 3 log 3 - log 2 - log 3

↪log x = 2 log 3

[ °.° m log a = log a^{m} ]

↪log x = log 3²

[ By comparing ]

↪ x = 9.

Answer 2

$\huge\mathfrak\red{Answer :) }$

If the base of both the logs are same , then

Log(2x+3)+Log(2x-3)=Log55

=>Log(4x²-9)=Log55

=>4x²-9=55

=>4x²-64=0

=>(2x+8)(2x-8)=0

$\huge\red{Hence, }$

x=4. x= -4