Approximate the function at the value of x to four decimal places. h ( x ) = log 4 ⁡ x − 2 log 8 ⁡ 1.2 x , x = 5.3

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Approximate the function at the value of x to four decimal places.   h  (  x  )  =      log    4    ⁡  x  −  2      log    8    ⁡  1.2  x  ,                 x  =  5.3

Szulikto · Accepted Answer

h  (  x  )  =      log    4    ⁡  x  −  2      log    8    ⁡  1.2  x  ,                 x  =  5.3The value of x to four decimal places:=?Logarithmic functions:      log    a    ⁡  x  =                    log        e            ⁡      x                      log        e            ⁡      a          log  ⁡      x    a    =  a  log  ⁡  xApproximating the given function:  h  (  x  )  =      log    4    ⁡  x  −  2      log    8    ⁡  1.2  x  …  …  x  =  5.3We use logarithmic properties as stated above to the given function:  h  (  x  )  =      log    4    ⁡  x  −  2      log    8    ⁡  1.2  x    h  (  x  )  =                    log        e            ⁡      x                      log        e            ⁡      4        −      log    8    ⁡  (  1.2      )    2        x    2    =                    log        e            ⁡      x                      log        e            ⁡      4        −      log    8    ⁡  (  1.44  )      x    2      =                    log        e            ⁡      x                      log        e            ⁡      4        −                    log        e            ⁡      1.44      (              x        2            )                      log        e            ⁡      8      Substituting the value of x=5.3 in the above function:We get:  h  (  x  )  =                    log        e            ⁡      (      5.3      )                      log        e            ⁡      4        −                    log        e            ⁡      (      1.44      )      (      28.09      )                      log        e            ⁡      8          =  1.2030  −                    log        e            ⁡      (      40.4496      )        0.9031      =  1.2030  −      1.6069    0.9031      =  1.2030  −  1.7793    =  −  0.5763The value of x to four decimal places is:x=-0.5763

Approximate the function at the value of x to four decimal places. h(x)=log_4 x-2 log_8 1.2x, x=5.3

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