Solve the Logarithms with a base of 10?

what steps do i take to solve this and then turn it into a base 10 log?

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  • Jim
    Lv 7
    2 years ago

    2^(-3 x) = 11^(-x - 5)

    Take reciprocals of both sides:

    2^(3x) = 11^(x + 5)

    Take the logarithm of both sides and use the identity log(a^b) = b log(a):

    3 log(2) x = log(11) (x + 5)

    Expand out terms of the right hand side:

    3 log(2) x = log(11) x + 5 log(11)

    Subtract x log(11) from both sides:

    (3 log(2) - log(11)) x = 5 log(11)

    Divide both sides by 3 log(2) - log(11):

    x = (5 log(11))/(3 log(2) - log(11))

  • alex
    Lv 7
    2 years ago

    Take log both sides

  • 2 years ago

    2^(-3x) = 11^(-x-5) =>

    2^(3x) = 11^(x+5) =>

    (3x) * log(2) = (x+5) * log(11) =>

    x * [3*log(2) - log(11)] = 5*log(11) =>

    x * [log(8/11)] = 5*log(11) =>

    x = 5*log(11)/log(8/11)

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