SOLUTION: If log 4=0.6021 and log 6=0.7782 find log 0.096

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Question 1110926: If log 4=0.6021 and log 6=0.7782 find log 0.096
Found 2 solutions by josgarithmetic, MathTherapy:
Answer by josgarithmetic(39847) About Me  (Show Source):
You can put this solution on YOUR website!
0.096=10%5E%28-3%29%2A4%2A24=4%2A4%2A6%2A10%5E%28-3%29

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log%28%280.096%29%29=log%28%284%2A4%2A6%2A10%5E%28-3%29%29%29

log%28%284%29%29%2Blog%28%284%29%29%2Blog%28%286%29%29%2B%28-3%29
From here, use what was given and compute.

Answer by MathTherapy(10895) About Me  (Show Source):
You can put this solution on YOUR website!
If log 4=0.6021 and log 6=0.7782 find log 0.096
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log 4 = 0.6021    ;     log 6 = 0.7782
log 0.096 = log+%28%2896%2F%221%2C000%22%29%29
                     = log (96) - log (1,000)
                     = log (16 * 6) - log (1,000)
                     = log (16) + log (6) - log (1,000)
                     = log (42) + log (6) - log (103)
                     = 2 log (4) + log (6) - 3
                     = 2(0.6021) + 0.7782 - 3 ---- Substituting 0.6021 for log (4), and 0.7782 for log (6)
                     = 1.2042 + .7782 - 3 = 1.9824 - 3 = - 1.0176