AM-335

Exponential and logarithmic equations

A Math · Secondary 3 · Hard · Exponential and logarithmic equations

Solve the simultaneous equations

5^x\cdot 2^y=1

and

5^{x+1}=2^{y-2}

.

$x=-\dfrac{\ln 2}{\ln 5},\ y=1$
$x=\dfrac{\ln 2}{\ln 5},\ y=1$
$x=-1,\ y=\dfrac{\ln 5}{\ln 2}$
$x=1,\ y=-\dfrac{\ln 5}{\ln 2}$

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