Zoho Logarithms Quiz -1

log 5^10 = 10 log 5 = 10\times 0.698 = 6.98 ~ 7 (approx)

Solution

{log_{7}}^{2401}

={log_{7}}^{7^4}

=4{log_{7}}^{7}

=4

Solution

{log_{5}}^{3x}=2

=>3x=5^2

=>3x=25

=>x=\frac{25}{3}

Solution

 \frac{log \sqrt{36}}{log 36}

= \frac{log 36^{\frac{1}{2}}}{log 36}

=\frac{\frac{1}{2} log 36}{log 36}

=\frac{1}{2}

Solution

{log_{x}}^{\sqrt{5}}= \frac{1}{2}

=>\sqrt{5}= x^{\frac{1}{2}}

=>5^{\frac{1}{2}}= x^{\frac{1}{2}}

=>x = 5

 {log_{7}}^{x^3}= 12

=> x^3 = 7^12

=>x^3 = (7^4)^3

=>x = 7^4

Solution:

{log_{11}}^{121} = 5x

=>{log_{11}}^{11^2} = 5x

=>2{log_{11}}^{11} = 5x

=>2 = 5x

=>x = \frac{2}{5}

\left ( \frac{\log a}{\log \sqrt{a}} \right )^3

=\left ( \frac{2\log a}{\log a} \right )^3

=2^3

=8

Solution

\log_{6}7776

=\log_{6}6^{5}

=5\log_{6}6                                                          

=5 x 1

=5

Solution

\log_{5}x=3

=>x=5^3

 

\log_{x}y=5

=>y=x^5

=>y=(5^3)^5

=>y=5^15