Question

if log5=0.69897 and log7=0.8451,and find the value of log1225​

Answer 1

Step-by-step explanation:

log1225 =log(5×5×7×7)

= log(5×7)^2

=2(log5+log7)

=2(0.69897+0.8451)

= 2(1.54407)

= 3.08814

Answer 2

Given: $log5 =0.69897, log7 =0.8451$.

To find: the value of $log1225.$

Solution:

Simplify $log1225.$

$\[\begin{array}{l}\log 1225 = \log \left( {5 \times 5 \times 7 \times 7} \right)\\ \Rightarrow \log 1225 = \log \left( {{5^2} \times {7^2}} \right)\\ \Rightarrow \log 1225 = \log {\left( {5 \times 7} \right)^2}\end{array}\]$

Apply$\[\log {a^b} = b\log a\]$.

$\[ \Rightarrow \log 1225 = 2\log \left( {5 \times 7} \right)\]$

Apply, $\[\log \left( {m \times n} \right) = \log m + \log n\]$.

$\[\begin{array}{l} \Rightarrow \log 1225 = 2\left( {\log 5 + \log 7} \right)\\ \Rightarrow \log 1225 = 2\left( {0.69897 + 0.8451} \right)\\ \Rightarrow \log 1225 = 2 \times 1.54407\\ \Rightarrow \log 1225 = 3.08814\end{array}\]$

Hence, the value of $log1225$ is $3.08814$.