Modern Math

Logarithms

Easy

If $y > 0,$ and $\log_{y}(x) = 4, \log_{10y} (25x) = 2$ hold, what is $y?$

None of these

✅ Correct Option: 1

From $\log_y(x) = 4$ :

$x = y^4$

From $\log_{10y}(25x) = 2$ :

$25x = (10y)^2$

$25x = 100y^2$

Substituting $x = y^4$ :

$25(y^4) = 100y^2$

$25y^4 = 100y^2$

Dividing both sides by $25y^2$ (since $y > 0$ ):

$\dfrac{25y^4}{25y^2} = \dfrac{100y^2}{25y^2}$

$y^2 = 4$

Since $y > 0$ :

$y = 2$

BMSAT Kozhikode 2025

Simplify the following: $\dfrac{1}{\log_{8}(x)} - \dfrac{1}{\log_{7}(x)} + \dfrac{1}{\log_{6}(x)} - \dfrac{1}{\log_{5}(x)} + \dfrac{1}{\log_{4}(x)} - \dfrac{1}{\log_{3}(x)} + \dfrac{1}{\log_{2}(x)}$

BMSAT Kozhikode 2026

If $\log_6 x + 2\log_{36} x + 3\log_{216} x = 9$ , then $x =$ ___

If y>0,y > 0,y>0, and log⁡y(x)=4,log⁡10y(25x)=2\log_{y}(x) = 4, \log_{10y} (25x) = 2logy​(x)=4,log10y​(25x)=2 hold, what is y?y?y?

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If $y > 0,$ and $\log_{y}(x) = 4, \log_{10y} (25x) = 2$ hold, what is $y?$