Answer:
q = 0.3423122683
Step-by-step explanation:
We can find the exact solution to the exponential equation using the following steps:
Step 1: Divide both sides by 26:
[tex](19=26(0.4)^{q})/26\\ \\19/26=0.4^q[/tex]
Step 2: Take the log of both sides:
[tex]log(19/26)=log(0.4^q)[/tex]
Step 3: Apply the power rule of logs to bring down q:
[tex]log(19/26)=q*log(0.4)[/tex]
Step 4: Divide both sides by log(0.4) to solve for q:
[tex]\frac{log(19/26)}{log(0.4)}=q\\ \\0.3423122683=q[/tex]
Therefore, the exact solution to the equation is q = 0.3423122683.
