Find out the value of log10(135), If a² +b² = 7ab

1. If a² +b² = 7ab , prove that 

2log(a+b) = log9 + loga + logb

Sol:

a² +b² = 7ab

Add both side 2ab , We get

a² +b²+ 2ab = 7ab+2ab

(a+b)² = 9ab

Now taking log both side, we get

log(a+b)² = log9ab

2log(a+b) = log9 +loga + logb.

2. Prove that

log 35/78 = log7+ log5 - log2- log3- log13

Sol: log 35/78

= log (5×7) - log (2×3×13)

=(log7+log5) - (log2+log3+log13)

[Note: log(mn)= logm+logn]

Or

log 35/78 = log7+ log5 - log2- log3- log13

3. Find out the value of log10(135)

Sol: We know that

log(m+n) = logm + logn

log10(135) = log10(3×3×3×5)

                     = log10(3³×5)

                     = log10(3³)+ log10(5)

                     = 3 × 0.4771 + 0.6990

                     = 1.4313+ 0.6990

                     = 2.133

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