7x302x1 How do I solve this using logs with steps written ou

7^x=30^2x-1

How do I solve this using logs with steps written out?

Solution

7^x=30^(2x-1)

Taking naturl log on both sides:

ln(7^x) = ln{ 30^(2x-1)}

Use the log property: ln(a^x) = x*ln(a)

x*ln7 = (2x-1)ln(30)

xln7 - 2xln(30) = - ln(30)

x( ln7 -2ln(30) ) = -ln(30)

x = ln(30)/( 2ln(30) - ln7 )

= 3.40 /4.856

x = 0.7