So, I have the equaton $\log_2 x = 1000000$
How do I isolate and solve for x? What is the inverse of a logarithm?
$\endgroup$ 54 Answers
$\begingroup$Generally
$$\log_b(x) = c$$
is solved though exponentiation in base $b$:
$$b^{\log_b(x)} = b^c$$
Hence
$$x = b^c$$
What you need is the condition: $x > 0$ otherwise the log does not exist.
In your case:
$$\log_2(x) = 1000000$$
$$x = 2^{1,000,000}$$
$\endgroup$ 2 $\begingroup$$$\log_2(x)= n \Rightarrow 2^n=x $$
$$2^{1,000,000} = x$$
$\endgroup$ $\begingroup$Raise $2$ to the power of each side of the equation:
$\log_2x=1000000\iff$
$2^{\log_2x}=2^{1000000}\iff$
$x=2^{1000000}$
$\endgroup$ $\begingroup$The inverse function of logarithm is the exponential. So the inverse function of $\log_2 x$ is $2^x$, so by your example; $$\log_2x=1000000\ \rightarrow \ x=2^{1000000}$$
$\endgroup$
