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Consider the equation

-2*10^(4x)=-300". "
Solve the equation for
x. Express the solution as a logarithm in base10.

x=
Approximate the value of
x. Round your answer to the nearest thousandth.

x~~

Consider the equation $\newline$ $-2 \cdot 10^{4 x}=-300 \text {. }$ $\newline$ Solve the equation for $x$ . Express the solution as a logarithm in base $10$ . $\newline$ $x=$ $\newline$ Approximate the value of $x$ . Round your answer to the nearest thousandth. $\newline$ $x \approx$

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Change of base formula

Full solution

Q. Consider the equation

\newline

-2 \cdot 10^{4 x}=-300 \text {. }

\newline

Solve the equation for

x

. Express the solution as a logarithm in base

10

.

\newline

x=

\newline

Approximate the value of

x

. Round your answer to the nearest thousandth.

\newline

x \approx

Isolate exponential term: First, we need to isolate the exponential term on one side of the equation. $\newline$ $-2 \cdot 10^{4x} = -300$ $\newline$ Divide both sides by $-2$ to get the exponential term by itself. $\newline$ $10^{4x} = \frac{300}{-2}$ $\newline$ $10^{4x} = -150$
Divide by $-2$ : We notice that the exponential equation cannot equal a negative number since an exponential function with a positive base ( $10$ in this case) always yields a positive result. Therefore, there is no solution to this equation.

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