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To four decimal places, log 102=0.3010 and log 109=0.9542. Evaluate the logarithm log 10 using these values. Do
not use a calculator.

User Saji
by
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1 Answer

2 votes

Answer: log 10 is approximately 1.2552.

Explanation:

To evaluate the logarithm log 10 using the given values of log 102 and log 109, we can use the property of logarithms that states:

log a (x * y) = log a (x) + log a (y)

Since we know that 10 can be expressed as the product of 102 and 109:

10 = 102 * 109

We can rewrite the logarithmic equation as:

log 10 = log (102 * 109)

Applying the property of logarithms mentioned earlier:

log 10 = log 102 + log 109

Substituting the given values:

log 10 ≈ 0.3010 + 0.9542

Calculating the sum:

log 10 ≈ 1.2552

Therefore, using the given values of log 102 and log 109, the value of log 10 is approximately 1.2552.

User Hassan Khademi
by
7.1k points
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