Calculate: 10^{x+1}-1=99

Expression: ${10}^{x+1}-1=99$

Move the constant to the right-hand side and change its sign

${10}^{x+1}=99+1$

Add the numbers

${10}^{x+1}=100$

Write the number in exponential form with the base of $10$

${10}^{x+1}={10}^{2}$

Since the bases are the same, set the exponents equal

$x+1=2$

Move the constant to the right-hand side and change its sign

$x=2-1$

Subtract the numbers

$x=1$