Question

log25=1.3979 and log27=1.4314 find log135​

Answer 1

Answer:

$\boxed{ log \: 135 = 2.13004}$

Explanation

Given

log 25 = 1.3979

log 27 = 1.4314

To Find

The value of log 135

Solution

From the identity

$log \: ab = log \: a + log \: b$

We can write

log 135 = log (15)(9)

log 135 = log 15 + log 9

log 135 = 1og (5)(3) + log 3²

$\boxed{log \: {a}^{m} = m \:log \: a }$

log 135= log 5 + log 3 + 2 log3 ----(1)

We have

log 27 = 1.4314

log 3³ = 1.4314

3 log 3 = 1.4314

$\boxed{ log \: 3 = 0.47713}$

Also

log 25 = 1.3979

log 5² = 1.3979

2 log 5 = 1.3979

$\boxed{ log \: 5 = 0.69865}$

Put the values in eq(1)

log 135 =0.69865+ 0.47713+ 2 (0.47713)

log 135 = 1.17578 + 0.95426

$\boxed{ log \: 135 = 2.13004}$