find the value of x for which 5^x÷5^-3=5^5
Answers
Answer:
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Answer:
Exact Form:
x = − 3 + ln ( 3128 ) ln ( 5 )
Decimal Form:
x = 2.00059619…
Step-by-step explanation:
5 x ÷ 5 − 3 − 3 = 5 ^5
Simplify each term.
5 x + 3 − 3 = 5^ 5
Raise 5 to the power of 5 .
5 x + 3 − 3 = 3125
Move all terms not containing x to the right side of the equation.
5 x + 3 = 3128
Take the natural logarithm of both sides of the equation to remove the variable from the exponent.
ln
(
5
x
+
3
)
=
ln
(
3128
)
Expand
ln
(
5
x
+
3
)
by moving
x
+
3
outside the logarithm.
( x + 3 ) ln ( 5 ) = ln ( 3128 )
Apply the distributive property.
x
ln
(
5
)
+
3
ln
(
5
)
=
ln
(
3128
)
Move all the terms containing a logarithm to the left side of the equation.
x
ln
(
5
)
+
3
ln
(
5
)
−
ln
(
3128
)
=
0
Move all terms not containing
x
to the right side of the equation.
Tap for more steps...
x
ln
(
5
)
= − 3 ln ( 5 ) + ln ( 3128 )
Divide each term by
ln ( 5 ) and simplify.
Tap for more steps...
x = − 3 + ln ( 3128 ) ln ( 5 )
The result can be shown in multiple forms.
Exact Form:
x = − 3 + ln ( 3128 ) ln ( 5 )
Decimal Form:
x = 2.00059619…