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Suppose that log2 = a and log3 = b
Solve for x in terms of a and b:
6^x = 10/3 - 6^-x

  • calculus-watch parentheses -

    Parentheses are not needed for fractions in type-set texts because it is graphically clear. When transferred to a one-line expression, parentheses are required around the numerator and denominator.

    I assume the question is as follows, which is different from what you posted because of the missing parentheses.

    6^x=10/(3-6^(-x)) ....(1)

    From log(2)=a, and log(3)=b,
    we deduce that
    ea=2, and

    cross multiply (1), assume 3≠6^(-x)
    3*6^x - 6^0 = 10 .... (6^0 = 1)
    3*6^x = 11
    6^x = 11/3
    take log on both sides
    x(log(2)+log(3) = log(11)-log(3)
    x = (log(11)-b)/(a+b)

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