Answer:
2 and 3.
Step-by-step explanation:
Four to the second power is 16.
Four to the third power is 64.
30 lies between 16 and 64, thus the exponent must lie between 2 and 3.
The solution to the equation [tex]4^x = 30[/tex] must lie between 2 and 3
The given exponential equation is:
[tex]4^x = 30[/tex]
To find the value of x, find the natural logarithm of both sides of the equation
[tex]ln 4^x =ln30\\\\xln4 = ln30\\\\1.39x = 3.4\\\\[/tex]
Divide both sides by 1.39
[tex]\frac{1.39x}{1.39} = \frac{3.4}{1.39} \\\\x = 2.45[/tex]
Since 2.45 falls between 2 and 3, we can conclude that the solution to the equation must lie between 2 and 3
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