how do you solve this equation?

Question

30(5^2x)-1=176

Answer 1

30(5^2x) - 1 = 176
30(5^2x) = 177
5^2x = 177/30
Now take the log to any base of both sides of this equation:
2x*log5 = log(177/30)
2x = log(177/30)/log5 = 1.1028
x = 0.5514

Answer 2

easy , you use log
and the formula log xy = logx +log y and log x^y = y log x

so log 176 = log 30 + 2x (log5) (1)

log 176 =2.2456,
log30 = 1.4771
log 5 = 0.6990

you find log x=0.55 and x= 3.54

Answer 3

30(5^2x)-1=176
=>30(5^2x)=176 + 1 = 177
=>(5^2x)= 177/30 = 59/10
Taking log on both the sides we get
=>log(5^2x)= log(59/10)
=>(2x)*log(5)= log(59/10)
=>(2x)= [log(59/10)] / [log(5)]
=>x=(1/2)*[log(59/10)] / [log(5)]
=>x = 0.5514

I hope that it is clear now.

All the best.

Answer 4

Use logirthms. x = 3.54