Solve the equation using logs: 4 ( 5 ) − 0.06 x = 3Find approximations to two decimal places for x.

Question

Solve the equation using logs:  4  (  5      )          −      0.06      x        =  3Find approximations to two decimal places for x.

hrikalegt15 · Accepted Answer

the first thing to do is to isolate the exponential, so you get:      5          −      .06      x        =      3    4       o  r         4    3    =      5          .06      x      then you can take the log (base 5) of both sides. i will use the equation on the right because i prefer to work with positive exponents. so:  .06  x  =      log          5        ⁡  (  4      /    3  )now, let&#039;s take care of that ugly log. some calculators can handle logs with weird bases, but many can&#039;t. here is a trick to solve them. use this equation:      log          a        ⁡  (  b  )  =            ln      ⁡      (      b      )              ln      ⁡      (      a      )      so, plugging that in and solving for x, you get:  x  =            ln      ⁡      (      4              /            3      )              ln      ⁡      (      5      )        (      1    .06    )a quick notation sidenote:  ln  ⁡  (  4      /    3  )  =  ln  ⁡  (  4  )  −  ln  ⁡  (  3  )so working it out, that&#039;s:  x  ≈      .28768    1.60944    (      1    .06    )  =  2.98

spockmonkeyqj · Accepted Answer

Step 1: Calculate the fraction 3/4 = 0.75Step 2:   L  O      G          10        (      5          −      0.06      x        )  =  L  O      G          10        (  0.75  )Step 3:   −  0.06  x  L  O      G          10        (  5  )  =  L  O      G          10        (  0.75  ) (Property of Logarithmic expressions)Step 4: Simply calculate x.

Solve the equation using logs: 4(5)^(-0.06x)=3 Find approximations to two decimal places for x.

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