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:

$log_10 35 = 1.5441$

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