Question

Help me on this question? log x-log 9=1

Answer 1

log(x) - log(9) = 1

Subtracting the logs of numbers gives you the log of
the quotient of the numbers.

Log(x) - log(9) is the log of (x/9).

So the equation says: log (x/9) = 1

Raise 10 to the power of each side: 10^(log of x/9) = 10^1

But 10^(log of x/9) is x/9, and 10^1 is 10.

So x/9 = 10

x = 90

Answer 2

`\log { x } -\log { 9 } =1\\ \\ \log { \left( \frac { x }{ 9 } \right) } =1\\ \\ \log _( 10 ){ \left( \frac { x }{ 9 } \right) } =1\\ \\ { 10 }^( 1 )=\frac { x }{ 9 } \\ \\ 9\cdot 10=x\\ \\ x=90`

This is because:


`\log _( a ){ \left( \frac { x }{ p } \right) } \\ \\ =\log _( a ){ \left( \frac { { a }^( m ) }{ { a }^( n ) } \right) } \\ \\ =\log _( a ){ \left( { a }^( \left( m-n \right) ) \right) } \\ \\ =\left( m-n \right) \cdot \log _( a ){ a } \\ \\ =m-n\\ \\ =\log _( a ){ x } -\log _( a ){ p } \\`