Can you use laws of logs to show that t = 10.8 when 4.8(0.86)^t = 0.5(1.06)^t

Thanks guyz

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Remember that log(a*b) = log(a) + log(b).
Remember log(a^b) = b*log(a).

4.8 * 0.86^t = 0.5 * 1.06^t
Take log of both sides.
log(4.8) + t*log(0.86) = log(0.5) + t*log(1.06)
Isolate t on one side.
log(4.8) - log(0.5) = t*(log(1.06) - log(0.86))
Solve for t.
t = [log(4.8) - log(0.5)] / [ log(1.06) - log(0.86)]
Evaluate the right side to get an approximation for t
t ≈ 0.98271233 / 0.09080741402
t ≈ 10.81708188
When rounded that gives
t ≈ 10.8