Question

100" alt=" - 6.2 ^{0.1x} = - 100" align="absmiddle" class="latex-formula">
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Answer 1

Answer:

$x=25.24$

Step-by-step explanation:

To find the value of $x$, we are solving the exponential equation $-6.2^{0.1x} =-100$ using logarithms.

Let's solve it step-by-step

Step 1. Divide both sides of the equation by -1 to get rid of the negative signs:

$-6.2^{0.1x} =-100$

$\frac{-6.2^{0.1x}}{-1} =\frac{-100}{-1}$

$6.2^{0.1x} =100$

Step 2. Take natural logarithm to bot sides of the equation:

$ln(6.2^{0.1x)}=ln(100)$

Step 3. Use the power rule for logarithms: $ln(a^{x} )=xln(a)$

For our equation: $a=6.2$ and $x=0.1x$

$ln(6.2^{0.1x)}=ln(100)$

$0.1xln(6.2)=ln(100)$

Step 4. Divide both sides of the equation by $0.1ln(6.2)$

$0.1xln(6.2)=ln(100)$

$\frac{0.1xln(6.2)}{0.1ln(6.2)} =\frac{ln(100)}{0.1ln(6.2)}$

$x=\frac{ln(100)}{0.1ln(6.2)}$

$x=25.24$

We can conclude that the value of x in our exponential equation is approximately 25.24.