Question

logarithm of x with base 32 is -1/5​

Answer 1

Answer:

log 32 ( x ) = 1 5

log₃₂x  + log₃₂(2⁻³) = 1/5

log₃₂x - 3log₃₂2 = 1/5

log₃₂x = 1/5 + 1/5

32^1/10 = x

x = √2

Answer 2

Given : logarithm of x with base 32 is -1/5​

$\log_{32}x=\dfrac{-1}{5}$

To Find :  Value of x

Solution:

$\log_{a}b=\frac{\log_{2}b}{\log_{2}a}$

Hence

$\log_{32}x=\dfrac{-1}{5}$

$\dfrac{\log_{2}x}{\log_{2}32}=\dfrac{-1}{5}$

32 = 2⁵

log aⁿ = nlog a

logₐa= 1

$\dfrac{\log_{2}x}{\log_{2}2^5}=\dfrac{-1}{5}$

$\dfrac{\log_{2}x}{5\log_{2}2}=\dfrac{-1}{5}$

$\dfrac{\log_{2}x}{5}=\dfrac{-1}{5}$

$\log_{2}x =-1$

=> x = 2⁻¹

=> x = 1/2

Hence value of x is 1/2

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