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If log a^(3/2) and log b are equal, find log a + log b.

Mathematics

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Answer

2.2

Step-by-step solution

2 steps

let's solve this logarithm problem.

  1. Use the given information to find the value of log⁡a\log a.

    We are given log⁡a2=3.2\log a^2 = 3.2.
    Using the logarithm property log⁡xn=nlog⁡x\log x^n = n \log x, we can rewrite the equation:

    2log⁡a=3.22 \log a = 3.2

    Divide both sides by 2 to find log⁡a\log a:

    log⁡a=3.22\log a = \frac{3.2}{2} log⁡a=1.6\log a = 1.6
  2. Use the value of log⁡a\log a and the given log⁡b\log b to find the required sum.

    We need to find log⁡a+log⁡b\log a + \log b.
    We found log⁡a=1.6\log a = 1.6 and we are given log⁡b=0.6\log b = 0.6.
    Substitute these values into the expression:

    log⁡a+log⁡b=1.6+0.6\log a + \log b = 1.6 + 0.6 log⁡a+log⁡b=2.2\log a + \log b = 2.2

    The final answer is 2.2.

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