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Evaluate log base square root of 19 of 6

$\log_{\sqrt{19}} (6)$

Step 1

Rewrite as an equation.

$\log_{\sqrt{19}} (6) = x$

Step 2

Rewrite

$\log_{\sqrt{19}} (6) = x$ in exponential form using the definition of a logarithm. If

$x$ and

$b$ are positive real numbers and

$b$ does not equal

$1$ , then

$\log_{b} (x) = y$ is equivalent to

$b^{y} = x$ .

${\sqrt{19}}^{x} = 6$

Step 3

Create equivalent expressions in the equation that all have equal bases.

${\sqrt{19}}^{x} = {\sqrt{19}}^{1.21704642}$

Step 4

Since the bases are the same, the two expressions are only equal if the exponents are also equal.

$x = 1.21704642$

Step 5

The variable

$x$ is equal to

$1.21704642$ .

$1.21704642$