How do you use #log10^5=.6990# and #log10^7=.8451# to evaluate the expression# log_10 35#?

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Answer 1 · 2016-05-03T23:02:17

Log form and index form are interchangeable.
Remember that logs are indices - the same laws apply.

If #a^b = c rArr log_a c = b#

Let's change from log from to index form first.

#log_10 5 = 0.6990 rArr 10^0.6990 = 5#
#log_10 7 = 0.8451 rArr 10^0.8451 = 7#

#35 = 5 xx 7 = 10^0.6990 xx 10^0.8451#

If the bases (10) are the same and you are multiplying, add the indices.

#10^1.5441 = 35# This is index form - change to log form:

#log_10 35 = 1.5441#