the solution of the equation is 2.23 ⇒ answer b
step-by-step explanation:
* lets revise the meaning of exponential function
- the form of the exponential function is y = ab^x, where a ≠ 0, b > 0 ,
b ≠ 1, and x is any real number
- it has a constant base b
- it has a variable exponent x
- to solve an exponential equation, take the log or ln of both sides,
and solve for the variable
* lets solve the problem
∵ ![7^{x}=77](/tex.php?f=7^{x}=77)
- the base is 7 and the exponent is x
- insert ㏑ in both sides
∴ ![ln(7^{x})=ln(77)](/tex.php?f=ln(7^{x})=ln(77))
- use the rule ![ln(a^{n})= nln(a)](/tex.php?f=ln(a^{n})= nln(a))
∴ x ㏑(7) = ㏑(77)
- to find x divide both sides by ㏑(7)
∴ ![x=\frac{ln(77)}{ln(7)}=2.23](/tex.php?f=x=\frac{ln(77)}{ln(7)}=2.23)
* the solution of the equation is 2.23 to the nearest 2 decimal places