Solving Exponential Equations (lacking a common base)

Solve the exponential equation: 7^g=14

g = 1.356207187

Step-by-step explanation:

7^g = 14

Take the log on both sides

log (7^g) = log 14

We know that log a^b = b log a

g log 7 = log 14

Divide each side by log 7

g log 7 / log 7 = log 14 / log 7

g = log 14 / log 7

g = 1.356207187

g = 1.356

Step-by-step explanation:

Use logs both sides

log (7^g) = log (7*2)

glog7 = log7 + log2

g = 1 + log2/log7

g = 1.3562071871