Solve the exponential equation by taking the logarithm on bo

Solve the exponential equation by taking the logarithm on both sides Express the solution set in terms of logarithms. Then use a calculator to obtain a decimal approximation tor the solution. 6^(x + 1) = 383 What is the solution in terms of logarithms? The solution set is (Use integers or decimals for any number in the expression)

Solution

Given that -----

6^(x+1) = 383

Now, taking natural logarithm on both side ---

log_e(6^x+1) = log_e(383)

Now. log_e(Mⁿ) = n×log_e(M)

So, (x+1)(log_e6) = log_e383

x+1 = log_e383/log_e6

x+1 = 5.948/1.792

x+1 = 3.32

x = 3.32-1

x = 2.32