a)Express the given quantity as a single logarithm. 1 3 ln ⁡ ( x + 2 ) 3 + 1 2 [ ln ⁡ ( x ) − ln ⁡ ( x 2 + 3 x + 2 ) 2 ]b) Solve each equation for x.1) e 5 − 4 x = 4x=?2) ln ⁡ ( 3 x − 13 ) = 8x=?

Question

a)Express the given quantity as a single logarithm.      1    3    ln  ⁡  (  x  +  2      )    3    +      1    2    [  ln  ⁡  (  x  )  −  ln  ⁡  (      x    2    +  3  x  +  2      )    2    ]b) Solve each equation for x.1)      e          5      −      4      x        =  4x=?2)   ln  ⁡  (  3  x  −  13  )  =  8x=?

Jeroronryca · Accepted Answer

a)Solution:      1    3    ln  ⁡  (  x  +  2      )    3    +      1    2    [  ln  ⁡  (  x  )  −  ln  ⁡  (      x    2    +  3  x  +  2      )    2    ]  =  ln  ⁡  (  x  +  2      )          3              /            3        +      1    2    ln  ⁡  x  −      1    2    ln  ⁡  (      x    2    +  3  x  +  2      )    2    =  ln  ⁡  (  x  +  2  )  +  ln  ⁡      x          1              /            2        −  ln  ⁡  (      x    2    +  3  x  +  2      )          2              /            2        =  ln  ⁡  (  x  +  2  )  (      x          1              /            2        )  −  ln  ⁡  (      x    2    +  3  x  +  2  )      [    ∵    ln    ⁡    a    +    ln    ⁡    b    =    ln    ⁡    a    b    ]    =  ln  ⁡            (              x                  3                      /                    2                    +      2              x                  1                      /                    2                    )              (              x        2            +      3      x      +      2      )            [    ∵    ln    ⁡    a    −    ln    ⁡    b    =    ln    ⁡          a      b        ]        Hence                1      3        ln    ⁡    (    x    +    2          )      3        +          1      2        [    ln    ⁡    x    −    ln    ⁡    (          x      2        +    3    x    +    2          )      2        ]        =    ln    ⁡                  (                  x                      3                          /                        2                          +        2                  x                      1                          /                        2                          )                    (                  x          2                +        3        x        +        2        )

Darryl English · Accepted Answer

b)Solution:1)      e          5      −      4      x        =  4  ⇒  5  −  4  x  =  ln  ⁡  4  ⇒  4  x  =  5  −  ln  ⁡  4  ⇒  x  =      5    4    −      1    4    ln  ⁡  42)  ln  ⁡  (  3  x  −  13  )  =  8  ⇒  3  x  −  13  =      e    8    ⇒  3  x  =  13  +      e    8  math xmlns=&quot;http://www.w3.org/1998/Math/MathML&quot;&amp;gt;  ⇒  x  =      1    3    (  13  +      e    8    )

Express the given quantity as a single logarithm. 1/3 ln(x+2)^3+1/2 [ln(x)-ln(x^2+3x+2)^2] Solve each equation for x. e^(5-4x)=4 x=? ln(3x-13)=8 x=?

Answered question

Answer & Explanation

New Questions in Calculus 1