(d) $$ \quad 3 \cdot\left(2^{x}\right)=0,3 $$

Question

UpStudy AI · Accepted Answer

Given the equation

3 · (2^x) = 0.3

we start by isolating 2^x. Divide both sides by 3:

2^x = 0.3 / 3  
  2^x = 0.1

Now, to solve for x, take the logarithm (using any base; here we'll use the natural logarithm):

ln(2^x) = ln(0.1)

Use the power rule for logarithms (ln(a^b) = b · ln(a)):

x · ln(2) = ln(0.1)

Solve for x by dividing both sides by ln(2):

x = ln(0.1) / ln(2)

Thus, the solution is

x = ln(0.1) / ln(2)  [exact form]

For a numerical approximation, note that:
  ln(0.1) ≈ -2.302585093
  ln(2) ≈ 0.693147181

Therefore:

x ≈ -2.302585093 / 0.693147181 ≈ -3.321928

So the final answer is:

x = ln(0.1) / ln(2)  or approximately x ≈ -3.322.
$$ x = \frac{\ln(0.1)}{\ln(2)} $$ or approximately $$ x \approx -3.322 $$.

(d) \( \quad 3 \cdot\left(2^{x}\right)=0,3 \)