Simplify without using a calculator.
1.) log3(log3(log3 27)

2.) e^ln 2-ln 6

3.) e^b ln a

4.) ln(3+x)-ln(x^2-9)

Question

Simplify without using a calculator. 
1.) log3(log3(log3 27)

2.) e^ln 2-ln 6

3.) e^b ln a

4.) ln(3+x)-ln(x^2-9)

solomonzelman · Answer

My closest interpretation.

$\LARGE\color{blue}{ \bf    log[~~~log_3(log_327)~~~] }$

$\LARGE\color{blue}{ \bf    log[~~~log_3(log_33^3)~~~] }$

$\LARGE\color{blue}{ \bf    log[~~~log_3(3log_33)~~~] }$

$\LARGE\color{blue}{ \bf    log[~~~log_3(3 \times 1)~~~] }$

$\LARGE\color{blue}{ \bf    log[~~~log_3(3 )~~~] }$

$\LARGE\color{blue}{ \bf    log[~~~1~~~] }$

$\LARGE\color{blue}{ \bf    log_{~any~~possible~~base~}1=0 }$

solomonzelman · Answer

$\LARGE\color{red}{ \bf     Log_vv=1 }$      $\large\color{red}{ \bf    (if~~v≠0,1,complex~num.~~,~~imaginary~) }$


$\LARGE\color{red}{ \bf     Log_cc^b=b \times Log_cc=b \times 1=b }$


$\LARGE\color{red}{ \bf     Log_v1=0 }$      $\large\color{red}{ \bf    (for~~any~~value~~of~~v.) }$

solomonzelman · Answer

questions 2 and 3 are unclear to me. I don't know how to intepret them, and 4....

$\LARGE\color{purple }{ \bf    ln(3+x)-ln(x^2-9)  }$


$\LARGE\color{purple }{ \bf    ln(x+3)-ln(x^2-9)  }$


$\LARGE\color{purple }{ \bf    ln \frac{(x+3)}{(x^2-9) } }$


$\LARGE\color{purple }{ \bf    ln \frac{(x+3)}{(x-3)(x+3) } }$


$\LARGE\color{purple }{ \bf    ln \frac{\cancel{ (x+3)} }{ \cancel{ (x+3)}(x-3) } }$


$\LARGE\color{purple }{ \bf    ln \frac{1}{(x-3) } }$