# Solve for y 5(2)^(3y)-4=13

5(2)3y-4=13
Remove parentheses.
5⋅23y-4=13
Move all terms not containing y to the right side of the equation.
Add 4 to both sides of the equation.
5⋅23y=13+4
5⋅23y=17
5⋅23y=17
Divide each term by 5 and simplify.
Divide each term in 5⋅23y=17 by 5.
5⋅23y5=175
Cancel the common factor of 5.
Cancel the common factor.
5⋅23y5=175
Divide 23y by 1.
23y=175
23y=175
23y=175
Take the natural logarithm of both sides of the equation to remove the variable from the exponent.
ln(23y)=ln(175)
Expand ln(23y) by moving 3y outside the logarithm.
3yln(2)=ln(175)
Divide each term by 3ln(2) and simplify.
Divide each term in 3yln(2)=ln(175) by 3ln(2).
3yln(2)3ln(2)=ln(175)3ln(2)
Simplify 3yln(2)3ln(2).
Cancel the common factor of 3.
Cancel the common factor.
3yln(2)3ln(2)=ln(175)3ln(2)
Rewrite the expression.
yln(2)ln(2)=ln(175)3ln(2)
yln(2)ln(2)=ln(175)3ln(2)
Cancel the common factor of ln(2).
Cancel the common factor.
yln(2)ln(2)=ln(175)3ln(2)
Divide y by 1.
y=ln(175)3ln(2)
y=ln(175)3ln(2)
y=ln(175)3ln(2)
y=ln(175)3ln(2)
The result can be shown in multiple forms.
Exact Form:
y=ln(175)3ln(2)
Decimal Form:
y=0.58851158…
Solve for y 5(2)^(3y)-4=13

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