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18 January, 15:53

Solve 4x+2 = 12 for x using the change of base formula

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  1. 18 January, 16:48
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    x=2.5

    Step-by-step explanation:

    We have,

    4x+2=12

    /implies4x=10

    Taking log both the sides we have,

    log/,4x=log/,10

    /implies log/,4 + log/, x=log/,10 / left/:/: [ / because log/, ab = log/, a + log/, b/right ]

    /implies log/, x=log/,10 - log/,4

    /implies log/, x={ log/, (/frac{10}{4}) / : /:/left [/because log/, a - log/, b = log/,/frac{a}{b} / right ]

    /implies log/, x=log/,2.5

    /implies / frac{log/, x}{log/,2.5}=1

    /implies log_{ (2.5) }/, x=1/:/:/left [ / because log_{b}/, a=/frac{log/, a}{log/, b} / right ]

    /implies x = (2.5) ^{1}/:/: [ / because log_{b}/, a=m / implies a=b^{m} ]

    Hence, we have x=2.5
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