Answer:
[tex]x=-2[/tex]
Step-by-step explanation:
[tex]log_{2x+7}(27)= 3[/tex]
We need to find the value of x
WE write the given log equation in exponential form'
[tex]log_b(a)=x[/tex] can be written as [tex]b^x=a[/tex]
Using this we convert log to exponential form
[tex]log_{2x+7}(27)= 3[/tex]
[tex](2x+7)^3= 27[/tex]
27 can be written as 3^3
[tex](2x+7)^3= 3^3[/tex]
Both sides have exponent 3. To remove exponent 3 we take cube root on both sides.
[tex]2x+7=3[/tex]
Subtract 7 on both sides
[tex]2x=-4[/tex]
Divide both sides by 2
[tex]x=-2[/tex]
