HCL Logarithms Quiz-1

Solution
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

Solution
{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}

Solution
\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