Answer :

To solve the equation [tex]\(16 \times (1.19^x) = 7 \times (1.13^x)\)[/tex], we'll go through the problem step by step:

1. Start with the equation:
[tex]\[
16 \times (1.19^x) = 7 \times (1.13^x)
\][/tex]

2. Take the logarithm on both sides:
[tex]\[
\log(16 \times (1.19^x)) = \log(7 \times (1.13^x))
\][/tex]

3. Apply the properties of logarithms:
- The logarithm of a product is the sum of the logarithms:
[tex]\[
\log(16) + \log(1.19^x) = \log(7) + \log(1.13^x)
\][/tex]
- The logarithm of an exponent is the exponent times the logarithm:
[tex]\[
\log(16) + x \cdot \log(1.19) = \log(7) + x \cdot \log(1.13)
\][/tex]

4. Rearrange terms to isolate [tex]\(x\)[/tex]:
[tex]\[
x \cdot \log(1.19) - x \cdot \log(1.13) = \log(7) - \log(16)
\][/tex]

5. Factor out [tex]\(x\)[/tex]:
[tex]\[
x \cdot (\log(1.19) - \log(1.13)) = \log(7) - \log(16)
\][/tex]

6. Solve for [tex]\(x\)[/tex]:
[tex]\[
x = \frac{\log(7) - \log(16)}{\log(1.19) - \log(1.13)}
\][/tex]

By evaluating the expression above, we find that:

[tex]\[
x \approx -15.9789
\][/tex]

So, the solution to the equation is approximately [tex]\(x = -15.9789\)[/tex].

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Rewritten by : Barada