Question

If log5 2 = log3m/log3n, then find the value of m and n.​

Answer 1

$\underline{\textbf{Given:}}$

$\mathsf{log_5\,2=\dfrac{log_3\,m}{log_3\,m}}$

$\underline{\textbf{To find:}}$

$\textsf{The value of m and n}$

$\underline{\textbf{Solution:}}$

$\mathsf{Consider,}$

$\mathsf{log_5\,2=\dfrac{log_3\,m}{log_3\,m}}$

$\textsf{Using the formula,}$

$\boxed{\mathsf{log_ab=\dfrac{1}{log_ba}}}$

$\mathsf{log_5\,2=log_3\,m{\times}log_n\,3}$

$\mathsf{log_5\,2=log_n\,3{\times}log_3\,m}$

$\textsf{Using the formula,}$

$\boxed{\mathsf{log_ac=log_ab{\times}log_bc}}$

$\mathsf{log_5\,2=log_n\,m}$

$\textsf{Comparing on bothsides, we get}$

$\boxed{\mathsf{m=2\;\;\&\;\;n=5}}$

$\underline{\textbf{Find more:}}$

log root a to the base b into log cube root b to the base e into log fourth root of c to the base is equal to

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Answer 2

Answer:m=2 and n=5

Step-by-step explanation:

we know that the log has base 10 in general so we convert base 5, base 3 into base 10 and the formula of converting the log is

log10 a\lob10b.

now ,

log10 2/log10 5=(log10 m/log10 3)/(log10 n/log10 3)

log10 2/log10 5=log10 m/log 10 n

log10(2/5)=log10(m/n)

so compare both side

m=2 and n=5