How do you solve $3^{2 x} = 75$ $3^(2x) = 75$ ?

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Answer 1 · 2016-01-29T10:26:25

$x = 1.9649735207179$ $x=1.9649735207179$

Start from the given equation:

$3^{2 x} = 75$ $3^(2x)=75$

Take the logarithm of both sides of the equation

${log}_{10} 3^{2 x} = {log}_{10} 75$ $log_10 3^(2x)=log_10 75$

$(2 x) \cdot {log}_{10} 3 = {log}_{10} 75$ $(2x)*log_10 3=log_10 75$

divide both sides of the equation by ${log}_{10} 3$ $log_10 3$

$\frac{(2 x) \cdot {log}_{10} 3}{{log}_{10} 3} = \frac{{log}_{10} 75}{{log}_{10} 3}$ $((2x)*log_10 3)/log_10 3=log_10 75/log_10 3$

$((2x)*cancel(log_10 3))/cancel(log_10 3)=log_10 75/log_10 3$

$2x=log_10 75/log_10 3$

$x=1/2*log_10 75/log_10 3$ the exact value

$color (red)(x=1.9649735207179$ the calculator value

Check: at $x=1.9649735207179$

$3^(2x)=75$

$3^((2*(1.9649735207179)))=75$

$75=75$

Have a nice day !!! from the Philippines...

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