Question

log 2 base e * log 25 base x = log 16 base 10 * log 10 base e , detect the value of x​

Answer 1

Answer:

Step-by-step explanation:

Answer 2

question is ....

$log_e2\times log_x25=log_{10}16\times log_e10$ then we have to find value of x.

we know from logarithm,

$log_ab=\frac{log_cb}{log_ca}$ where c ≠ 1, c > 0

so, we can write $log_e2=\frac{log_{10}2}{log_{10}e}$

$log_x25=\frac{log_{10}25}{log_{10}x}$

$log_e10=\frac{log_{10}10}{log_{10}e}=\frac{1}{log_{10}e}$

now, using all above resolutions in expression,

$\frac{log_{10}2}{log_{10}e}\times\frac{log_{10}25}{log_{10}x}=log_{10}16\times\frac{1}{log_{10}e}$

$\frac{log_{10}2\times log_{10}25}{log_{10}x}=log_{10}16$

$\left(\frac{log_{10}2}{log_{10}x}\right)=\frac{log_{10}16}{log_{10}25}$

$log_x2=log_{25}16$

$log_x2=log_{5^2}(4^2)$

we know, $log_{a^m}x^n=\frac{n}{m}log_ax$

so, $log_{5^2}(4^2)=\frac{2}{2}log_54$

so, $log_x2=log_54$

or, $log_x2=log_{(\sqrt{5})^2}(2^2)$

or, $log_x2=log_{\sqrt{5}}2$

comparing both sides,

x = √5