Question

If log 2 = 0-3010 and lo3-04771, then the value of log (3240) will be

Answer 1

Step-by-step explanation:

Given :-

log 2 = 0.3010

log 3= 0.4771

To find :-

Find the value of log 3240 ?

Solution:-

Given number = log 3240

3240 = 2×1620

3240 = 2×2×810

3240 = 2×2×2×405

3240 = 2×2×2×3×135

3240 = 2×2×2×3×3×45

3240 = 2×2×2×3×3×3×15

3240 = 2×2×2×3×3×3×3×5

3240 = 2³×3⁴×5

log 3240 = log ( 2³×3⁴×5)

We know that

log ab = log a + log b

=> log 3240 = log 2³ + log 3⁴ + log 5

We know that

log a^m = m log a

=> log 3240 = 3 log 2 + 4 log 3 + log 5

=>log 3240=3(0.3010)+4(0.4771)+(0.6990)

=> log 3240 = 0.9030 +1.9084+0.6990

=> log 3240 = 3.5104

Answer:-

The value of log 3240 for the given problem is 3.5104

Used formulae:-

• log 2 = 0.3010
• log 3= 0.4771
• log 5 = 0.6990
• log ab = log a + log b
• log a^m = m log a