Algebra Examples

$10^{t + 1} = 50$

Step 1

Take the base $10$ logarithm of both sides of the equation to remove the variable from the exponent.

$\log (10^{t + 1}) = \log (50)$

Step 2

Expand the left side.

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Step 2.1

Expand $\log (10^{t + 1})$ by moving $t + 1$ outside the logarithm.

$(t + 1) \log (10) = \log (50)$

Step 2.2

Logarithm base $10$ of $10$ is $1$ .

$(t + 1) \cdot 1 = \log (50)$

Step 2.3

Multiply $t + 1$ by $1$ .

$t + 1 = \log (50)$

Step 3

Subtract $1$ from both sides of the equation.

$t = \log (50) - 1$

Step 4

The result can be shown in multiple forms.

Exact Form:

$t = \log (50) - 1$

Decimal Form:

$t = 0.69897000 \dots$