maths

Given that x=lg a is a solution of the equation 10^(2x+1)-7(10^x) =26. Find the value of a.

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  1. 10 *(10^x)^2 - 7 (10^x) = 26

    let z = 10^x

    10 z^2 - 7 z -26 = 0

    ( z - 2)( 10 z + 13) = 0

    10^x = 2 or 10^x = -1.3

    if you log is base 10

    log 10^x = x = log 2

    but if x = log a
    then log a = log 2
    so a = 2

    similarly
    log 10^x = x = log (-1.3) but not allowed :)

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    posted by Damon

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