How do you write ${log}_{5} (625) = x$ $log_5(625)=x$ in exponential form?

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Answer 1 · 2015-06-18T21:49:08

$5^{x} = 625$ $5^x=625$
$x = 4$ $x=4$

The definition of a logarithm says :

${log}_{b} x = y \Leftrightarrow b^{y} = x$ $log_bx=y iff b^y=x$

In other words you can say that logarithm is the exponent to which you must raise the base $(b)$ $(b)$ to get number $x$ $x$ .

In this case $x$ $x$ is the exponent to which you have to raise base (5) to get 625

$5^{x} = 625$ $5^x=625$
This is the exponential form.

To find the answer you have to count which power of 5 is 625

$5^{1} = 5$ $5^1=5$
$5^{2} = 5 \cdot 5 = 25$ $5^2=5*5=25$
$5^{3} = 25 \cdot 5 = 125$ $5^3=25*5=125$
$5^{4} = 125 \cdot 5 = 625$ $5^4=125*5=625$

$5^{4} = 625$ $5^4=625$ so $x = 4$ $x=4$

How do you write log5(625)=xlog_5(625)=x in exponential form?