WILL MARK AS BRAINLIEST Part 1.] Match the y-coordinate with the given x-coordinate for the equation y=log_{10} x

Question

WILL MARK AS BRAINLIEST

Part 1.] Match the y-coordinate with the given x-coordinate for the equation y=log_{10} x
1.) 1/100. A.) 0
2.) 1/10. B.) -2
3.) 1. C.) 2
4.) 10. D.) -1
5.) 100. E.) 1

Part 2.] Match the y-coordinate with the given x-coordinate for the equation y=log_{2} x
1.) 8. A.) 2
2.) 4. B.) 1
3.) 2. C.) 3
4.) 1. D.) 0
5.) 1/2. E.) -1

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    2021-09-09T17:44:19+00:00

    These are two parts with 5 questions each.

    Part 1.] Match the y-coordinate with the given x-coordinate for the equation y=log_{10}x

    If you use this property you can match all the coordinates:

    log_{a}a^{x}=x

    Because that means that:  log_{10}(10)^{x}=x

    So, just write each x-coordinate as a power of 10.

    1.) 1/100 = 10^(-2)
    2.) 1/10 = 10 ^ (-1)
    3.) 1 = 10 ^ (0)
    4.) 10 = 10^(1)
    5.) 100 = 10^(2)

    With that  you find:

    x-coordinate     y-coordinate
                             y=log_{10}x

    1/100                log_{10}(1/100) = - 2 => 1) matches B)

    1/10                  log_{10}(1/10)=-1 => 2) matches D)

    1                       log_{10}1=0 => 3) matches A)

    10                     log_{10}10=1 => 4) matches E)

    100                   log_{10}100=2 => 5) matches C)

    Part 2.] Match the y-coordinate with the given x-coordinate for the equation y=log_{2}x

    Using the same property of logarithms: log_{2}2^{x}=x

    And:

    1.) 8 = 2^(3)

    2.) 4 = 2^(2)

    3.) 2 = 2^(1)

    4.) 1 = 2^(0)

    5.) 1/2 = 2^(-1)

    So:

    x                y = y=log_{2}x

    8                y=log_{2}8=3 => matches C)

    4                 log_{2}4=2=> matches A)

    2                 log_{2}2=1 => matches B)
     
    1
                     log_{2}1=0 => matches D)

    1/2              log_{2}(1/2)=-1 => matches E)

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