Find the logarithm of 5832 to the base ³✓2 ya (3✓2).

1.Find the logarithm of 5832 to the base ³✓2 ya (3✓2).

Sol:

Let log 3✓2(5832) = x then by definition we get

(3✓2)^x = 5832 = 8 × 729 = 2³ × 3⁶

Or,

(3✓2)^x = [(✓2)²]³ × 3⁶

               = (✓2)⁶ × 3⁶ = (3✓2)⁶

(3✓2)^x = (3✓2)⁶ =⟩ x = 6

2. If log10(55) = 1.7404

        log10(93) = 1.9685

Find

(I) log10 55 × 93

Sol: (I) log10 55 × 93

            = log10 55 + log10 93

            = 1.7404 + 1.9685

            = 3.7089

3. If log10(3) = .4774 and 

log10(2) = .3010 then find log2(3).

Sol: We have

log2(3) = log10(3) / log10(2)

log2(3) = .4771 / .3010

log2(3) = 1.5850

4. Find the value of log8 (128).

Sol: log8 (128) = log8⁷/³ (8⁷/³ = 128)

         log8 (128) = ⁷/³log 8⁸

                             = 7/3 × 1 = 7/3

(Loga^a = 1)

5. Evaluate:

log10(81) / log10 (27)

Sol:

log10(81) / log10(27) = log10(3⁴) / log10 (3³)

log10(81) / log10(27) = 4log10³/3log10³

log10(81) / log10(27) = 4/3

log10(81) / log10(27) = 1.33

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