Struggling to finish an exponential equationI have this exponential equation I tried solving but I'm stuck at the end.The problem is this: 4 x − 3 x − 1 2 = 3 x + 1 2 − 2 2 x − 1 And my approach is this: 2 2 x + 2 2 x − 1 = 3 x + 1 2 + 3 x − 1 2 2 2 x ( 1 + 2 − 1 ) = 3 x ( 3 1 2 + 3 − 1 2 ) 2 2 x ∗ 3 2 = 3 x ( 3 + 1 3 ) 2 2 x ∗ 3 2 = 3 x ( 3 2 + 1 3 ) 2 2 x ∗ 3 2 = 3 x ∗ 4 3 3 --&gt; here I have rationalized the fraction 2 2 x 3 x = 4 3 3 ∗ 2 3 ( 2 2 3 ) x = 8 3 9 Now I hope I didn't make an error. How should I proceed from this point? Is there another way around this problem?

Question

Struggling to finish an exponential equationI have this exponential equation I tried solving but I&#039;m stuck at the end.The problem is this:      4    x    −      3          x      −              1        2              =      3          x      +              1        2              −      2          2      x      −      1      And my approach is this:      2          2      x        +      2          2      x      −      1        =      3          x      +              1        2              +      3          x      −              1        2                  2          2      x        (  1  +      2          −      1        )  =      3    x        (          3                        1          2                      +          3              −                  1          2                      )        2          2      x        ∗      3    2    =      3    x        (          3        +          1              3              )        2          2      x        ∗      3    2    =      3    x    (                              3                2            +      1              3        )      2          2      x        ∗      3    2    =      3    x    ∗            4              3              3  --&amp;gt; here I have rationalized the fraction            2              2        x                    3      x        =            4              3              3    ∗      2    3              (                        2          2                3            )        x    =            8              3              9  Now I hope I didn&#039;t make an error. How should I proceed from this point? Is there another way around this problem?

Maleah Lester · Accepted Answer

I think you did not make a mistake.Your last equation it&#039;s            (              2                  3                    )              2      x        =            (              2                  3                    )        3  because            8              3              9    =            8              3                            8            1        =      8          27        =            2      3                      3        3              =            2      3                      (                  3                )            3        =            (              2                  3                    )        3    .

Struggling to finish an exponential equation I have this exponential equation I tried solving but I'm stuck at the end. The problem is this: 4^x-3^(x-1/2)=3^(x+1/2)-2^(2x-1)

Answered question

Answer & Explanation

New Questions in Pre-Algebra