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Solve the logarithmic equation $\log_{x}\left(100\right)-\log_{x}\left(25\right)=2$

Step-by-step Solution

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Solution

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Final answer to the problem

$x=2$
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Step-by-step Solution

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Learn how to solve logarithmic differentiation problems step by step online. Solve the logarithmic equation logx(100)-logx(25)=2. The difference of two logarithms of equal base b is equal to the logarithm of the quotient: \log_b(x)-\log_b(y)=\log_b\left(\frac{x}{y}\right). Change the logarithm to base x applying the change of base formula for logarithms: \log_b(a)=\frac{\log_x(a)}{\log_x(b)}. If the argument of the logarithm (inside the parenthesis) and the base are equal, then the logarithm equals 1. Take the reciprocal of both sides of the equation.

Final answer to the problem

$x=2$

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Function Plot

Plotting: $\log_{x}\left(100\right)-\log_{x}\left(25\right)-2$

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◻2
◻◻
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◻√◻
◻√
∞
e
π
ln
log
log◻
lim
d/dx
D□x
∫
∫◻
|◻|
θ
=
>
<
>=
<=
sin
cos
tan
cot
sec
csc

asin
acos
atan
acot
asec
acsc

sinh
cosh
tanh
coth
sech
csch

asinh
acosh
atanh
acoth
asech
acsch

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Similar Problems Solved

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$\log_x\left(\frac{1}{8}\right)=-3$

$\log_x\left(100\right)-\log_x\left(25\right)=2$

$\log_2\left(x\right)-\log_2\left(10\right)=\log_2\left(9.3\right)$

$\log\left(\left(y+2\right)\right)=1+\log\left(\left(2y-6\right)\right)$

Main Topic: Logarithmic Differentiation

The logarithmic derivative of a function f(x) is defined by the formula f'(x)/f(x).

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