B) Solve the Folle 1) $$ 5.9^{x-1}=5 $$ $$ +15.125^{x+3}=\frac{1}{25} $$

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Solve the equation by following steps:
- step0: Solve for $$x$$:
  $$5.9^{x-1}=5$$
- step1: Convert the expressions:
  $$\left(\frac{59}{10}\right)^{x-1}=5$$
- step2: Take the logarithm of both sides:
  $$\log_{\frac{59}{10}}{\left(\left(\frac{59}{10}\right)^{x-1}\right)}=\log_{\frac{59}{10}}{\left(5\right)}$$
- step3: Evaluate the logarithm:
  $$x-1=\log_{\frac{59}{10}}{\left(5\right)}$$
- step4: Move the constant to the right side:
  $$x=\log_{\frac{59}{10}}{\left(5\right)}+1$$
Solve the equation $$ 15.125^{x+3}=\frac{1}{25} $$.
Solve the equation by following steps:
- step0: Solve for $$x$$:
  $$15.125^{x+3}=\frac{1}{25}$$
- step1: Convert the expressions:
  $$\left(\frac{121}{8}\right)^{x+3}=\frac{1}{25}$$
- step2: Take the logarithm of both sides:
  $$\log_{\frac{121}{8}}{\left(\left(\frac{121}{8}\right)^{x+3}\right)}=\log_{\frac{121}{8}}{\left(\frac{1}{25}\right)}$$
- step3: Evaluate the logarithm:
  $$x+3=\log_{\frac{121}{8}}{\left(\frac{1}{25}\right)}$$
- step4: Simplify:
  $$x+3=-2\log_{\frac{121}{8}}{\left(5\right)}$$
- step5: Move the constant to the right side:
  $$x=-2\log_{\frac{121}{8}}{\left(5\right)}-3$$
Let's solve the two equations step by step.

### 1) Solve $$ 5.9^{x-1}=5 $$

To solve this equation, we can rewrite it in logarithmic form:

$$
x - 1 = \log_{5.9}(5)
$$

Thus, we can express $$ x $$ as:

$$
x = \log_{5.9}(5) + 1
$$

### 2) Solve $$ 15.125^{x+3}=\frac{1}{25} $$

Similarly, we can rewrite this equation in logarithmic form:

$$
x + 3 = \log_{15.125}\left(\frac{1}{25}\right)
$$

Now, we can express $$ x $$ as:

$$
x = -3 - \log_{15.125}\left(\frac{1}{25}\right)
$$

### Final Results

1. For the first equation:
   $$
   x = \log_{5.9}(5) + 1
   $$

2. For the second equation:
   $$
   x = -2\log_{15.125}(5) - 3
   $$

These are the solutions for the given equations.
Solutions for the equations are: 1. $$ x = \log_{5.9}(5) + 1 $$ 2. $$ x = -2\log_{15.125}(5) - 3 $$

B) Solve the Folle 1) \( 5.9^{x-1}=5 \) \( +15.125^{x+3}=\frac{1}{25} \)

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