Apply the power rule of logarithms, which states that (a^b) = b a.

Mathematics

ScanSolve AI Answer

Answer

A. 0.3522\text{A. } 0.3522

Step-by-step solution

7 steps

To find the value of log⁡(1.5)2\log(1.5)^2, we will use the given values of log⁡2\log 2 and log⁡3\log 3 and properties of logarithms.

  1. Apply the power rule of logarithms, which states that log⁡(ab)=blog⁡a\log(a^b) = b \log a.

    log⁡(1.5)2=2log⁡(1.5)\log(1.5)^2 = 2 \log(1.5)

  2. Express 1.5 as a fraction using the numbers 2 and 3.

    1.5=321.5 = \frac{3}{2}

  3. Substitute the fractional form into the expression.

    2log⁡(32)2 \log\left(\frac{3}{2}\right)

  4. Apply the quotient rule of logarithms, which states that log⁡(ab)=log⁡a−log⁡b\log\left(\frac{a}{b}\right) = \log a - \log b.

    2(log⁡3−log⁡2)2 (\log 3 - \log 2)

  5. Substitute the given values log⁡2=0.3010\log 2 = 0.3010 and log⁡3=0.4771\log 3 = 0.4771.

    2(0.4771−0.3010)2 (0.4771 - 0.3010)

  6. Perform the subtraction inside the parentheses.

    2(0.1761)2 (0.1761)

  7. Perform the multiplication.

    2×0.1761=0.35222 \times 0.1761 = 0.3522

    The value of log⁡(1.5)2\log(1.5)^2 is 0.3522. This corresponds to option A.

    The final answer is A. 0.3522\text{A. } 0.3522.

Was this helpful?

Try one yourself

A new problem that tests the same skill.

Still stuck on this one?

Ask a follow-up, and the answer starts from this question.

Got a different question?Ask your own question

More Mathematics Questions

QApply the logarithm property a + b = (ab).QUse the logarithm property a − b = (a)/(b) to combine the terms on the left side.QSimplify the numerator using the logarithm property aⁿ = n a.QApply the power rule (ab)ⁿ = aⁿ bⁿ and (a^m)ⁿ = a^mn to the numerator.QApply the exponent rule ((a)/(b))ⁿ = (aⁿ)/(bⁿ) to the second term.
Browse by topic:Pre-Calculus
See all Mathematics questions →
Got a syllabus? Photograph it and I'll tell you what's due and what's worth the most.