Find the x-intercept of: 3 − 4 log 10 ⁡ ( 2 x ) My process: 4 log 10 ⁡ ( 2 x ) = 3 log 10 ⁡ ( 2 x ) = 3 4 How would I find the x-intercept from here? log 10 ⁡ ( 2 x ) = log 10 ⁡ ( ? ) 2x=?xintercept=(?)/(2)How do I find the x-intercept?

Question

Find the x-intercept of:  3  −  4      log          10        ⁡      (    2    x    )  My process:  4      log          10        ⁡      (    2    x    )    =  3      log          10        ⁡      (    2    x    )      =        3    4  How would I find the x-intercept from here?      log          10        ⁡      (    2    x    )      =        log          10        ⁡      (    ?    )    2x=?xintercept=(?)/(2)How do I find the x-intercept?

Julius Haley · Accepted Answer

You can write      log          10        ⁡  (  2  x  )  =      log          10        ⁡      10          3              /            4

Leanna Jennings · Accepted Answer

Let  f  (  x  )  =  3  −  4      log          10        ⁡      (    2    x    )  and set  f  (  x  )  =  0which gives  3  =  4      log          10        ⁡  (  2  x  )      3    4    =      log          10        ⁡  (  2  x  )Now       log    a    ⁡  b  =  c implies       a    c    =  b or like you have done       log          10        ⁡  (  2  x  )  =      log          10        ⁡      10          3              /            4       which gives      10          3              /            4        =  2  x  x  =            10              3                  /                4              2

Find the x-intercept of: 3- 4 log_(10)(2x)

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