Question

if log2=p , log5=q then log50=​

Answer 1

Anѕwєr :

$\boxed{ \huge \sf\orange{2q + p}}$

Exρlαnαtion:

Here, we are been asked to calculate the value of log50 where, log2 = p and log5 = q. Now we are gonna find the value of log50 by using Logarithm properties. Let's see the properties of Logarithms.

$\: \boxed{ \large \sf \orange{logmn \: = logm \: + logn}}$

$\: \: \: \: \: \boxed{ \large \sf \orange{logm {}^{n} = n \: logm}}$

Now, writing 50 interms of 2 and 5 .

>> 50 can be written as follows : 5² × 2

$\longrightarrow \: \sf \: log50 = log \bigg({{5}^{2} \times 2 } \bigg)$

Now using the first property It can be written as..

$\longrightarrow \: \sf \: log50 = log5 {}^{2} + log2$

Using the 2nd property of log5² can be written as 2log5

$\longrightarrow \: \sf \: log50 =2 log5 + log2$

$\longrightarrow \: \sf \: log50 =2 q + p$

_______________________________

Lєαrn Morє ::

Few properties of Logarithms:-

$\: \: \: \: \sf \: log_x \: \bigg( \dfrac{m}{n} \bigg) = logm_x \: - logn_x$

$\: \: \sf \: logb_b \: = 1$

$\: \: \sf \: log1_b \: = 0$

$\: \: \sf \: b {}^{logk_b} = k$

$\: \sf \: log_b \: b {}^{k} = k$

Answer 2

Answer:

Exapand log 50

$\rightarrow \tt \: log(5 \times 2 \times 5) \\ \\ \rightarrow \tt \: log(5) + log(2) + log(5) \\ \\ \rightarrow \tt \: q + p + q \\ \\ \rightarrow \tt \: 2q + p$