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

1 answer

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
Similar Questions
    1. answers icon 1 answer
  1. Which fact converts centigrams to kilograms?Use the prefix table to help you. milli- (m) centi- (c) deci- (d) base deca- (da)
    1. answers icon 1 answer
  2. 1. 1/3log base 8 of (x+1)=2log base 8 of 3-(2/3)log base 8 of (x+1)2. 2^x+8 times 2^=x all over 2 = 3 3. if log base a of 3= x
    1. answers icon 3 answers
    1. answers icon 1 answer
more similar questions