How do I rearrange to find X with this equation?

Jul 2019
1
0
uk
Hi,

I have been using the below equation to calculate Watts required to reach a reference level Sound Pressure Level (SPL), however I cannot seem to successfully rearrange equation to find required Lsens. Can anyone help and show me how to rearrange this so that X (or in this case Lsens) is the subject?

Equations used to calculate the Watts:
dBW = Lreq - Lsens + 20 * Log (D2/Dref) + HR
W = 10 to the power of (dBW / 10)

Where:
Lreq = 105 SPL (required SPL at listener)
Lsens = 89dB (loudspeaker sensitivity (1W/1m))
D2 = 2.5m (loudspeaker-to-listener distance)
Dref = 1.0m (reference distance)
HR = 0dB (desired amplifier headroom)
dBW = (ratio of power referenced to 1 watt)
W = 249W (power required)
 
Apr 2014
1,013
348
UK
OK, starting with:
dBW = Lreq - Lsens + 20 * Log (D2/Dref) + HR

Add Lsens to both sides:
dBW + Lsens = Lreq + 20 * Log (D2/Dref) + HR

Subtract dBW from both sides:
Lsens = Lreq - dBW + 20 * Log (D2/Dref) + HR