precalc help

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Find the exact value without a calc

1. log base 3 of 8 times log base 8 of 9. I started by changing both bases to 10 but don't know what to do from there.

2. e ^ log base e^2^9. I hope that isnt confusing. My teacher said we are suppose to get the bases all e, but how because there is only 1 log.

Suppose that ln 2= a and ln 3= b. Use the properties of logs to write each in terms of a and b

1. ln .5

thanks

  • precalc help -

    recall that
    log_a(n) = log_b(n)/log_a(b)
    log_a(n) = 1/log_n(a)

    1.
    log_3(8) * log_8(9)
    = 1/log_8(3) * log_8(9)
    = log_3(9)
    = 2

    2.
    recall that
    e^ln(n) = n, so
    e^ln(2^9) = 2^9 = 512

    3.
    .5 = 1/2, so
    ln .5 = ln(2^-1) = -ln(2) = -a

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